Not because they've got the biggest TV I've ever seen. Or, as Jack is quick to point out, because they're halfway through a refurbishment and it's a bit dusty. Or even because it's so toasty warm.
No, it's because there are cats everywhere. Wooden cats, plastic cats, metal cats, what look suspiciously like papier-mache cats, and 11 real cats, lolling around, fiddling about in their fleecy beds, stalking across the dining room table, tip-toeing over the computer keyboard and running up and down the slatted stairs to the attic extension.
Oh yes, and none of them has any fur. At all. Which is rather unnerving, as they stare, pinky-grey and strangely unblinking, from all round the bungalow, every so often jumping down and playing with a toy mouse or a ball, or just generally pottering about, blissfully unaware of the drama that has been revolving around them in the Cat Fancy world.
Because this is the hairless Sphynx cat. After nearly 40 years in the cat show wilderness and an awful lot of campaigning by besotted owners, it has finally been recognised as a breed by the Governing Council of the Cat Fancy - the feline equivalent of the Kennel Club. With the result that, as the GCCF put it: 'Sphynx cats will now be acceptable on our show benches.'
'About b****y time, too,' snorts Jack Cockrell, 62, a retired oil field consultant. 'It's a disgrace it didn't happen sooner. Just look at Darcy Bussell here - she's only eight months, but she's already championship material. Isn't she the most beautiful thing?'
Not for nothing have Sphynx cats been described as the Marmite of cats - you either love them (very fiercely), as the Cockrells and all members of the Sphynx Cat Association do, or you give a shudder and stare rather rudely, as I do.
It's hard not to, because they look extraordinary. You can see every bump and bone, every pimple and blemish. Their ears are enormous, their necks are so slim they look ready to snap in two, their eyes are HUGE. The faces look like something a special effects department has laboured over, their tummies are soft and rounded after lunch and their tails are long and rat-like.
Even so, to Jack and Phyllis, 59, they're just perfect. 'They're so sociable and friendly - they'll sit on your lap and jump on your shoulder and ride around for ages like a parrot,' says Jack.
'Of course they're totally mollycoddled, but they're nothing like normal pets. They're wonderful, but they do sort of take over.'
Indeed.
This is not the sort of pet you can placate with a tin of cat food and bowl of water. Oh no. These cats need a small and highly dedicated staff to cater for their peculiarities - most of which stem from their unnervingly smooth skin. For starters, they have a bit of a personal hygiene problem - without fur to absorb it, their skin can get rather oily.
So there's the regular bath night, Phyllis's responsibility (Jack does the litter trays, and most of the chat), which involves a shampoo and scrub in the bath, a good clean of the ears, a nail trim and a rub dry with a warm, fluffy towel.
The lack of a fur coat also means they need more protein to maintain their body temperature. So this lot are fed on £40 worth of top-quality biscuits, a couple of nice fresh roast chickens and 'a bit of fish or meat for a treat' each week.
And there'll be no popping outside at night for a bit of mouse-catching and a miaow at the Moon, because they'd freeze to death in ten minutes on a cold November night. So they need to have plenty of toys and, ideally, a small indoor climbing frame and an owner with a lot of patience to keep them exercised and entertained.
'We do sometimes put them in a harness and long lead and let them out in the garden in the summer,' says Jack. But only after they've been applied liberally with special suncream, obviously.
The more you look at them, the more they look like some sort of weird prehistoric beast. But they're relative babies on an evolutionary scale.
Hairless cats have popped up every so often all over the world since 1830, but the modern Sphynx descends from hairless kittens born in Canada in the Sixties and Seventies, after which they were exported to Europe.
Twenty-five years on, the Sphynx finally have championship status and there's a whole Sphynxr-elated world out there. There are at least 25 certified breeders in the UK - operating under names such as No Coat On, Streakers, BuffNaked, Baldesque and Misfits - and dozens more further afield: America, Australia, Russia, Kazakhstan.
Kittens are shipped from country to country for breeding purposes.
There are also countless websites, chat forums and goodness knows how many proud photographs of the strange-looking creatures posted on the internet.
And while Jack and Phyllis might seem pretty obsessed - there are even four kittens mewling in a basket in their bedroom - they're nothing compared to some owner-breeders.
Such as Kelly Hampton, 24, who lives in Wiltshire with her window-fitter husband Toby, 34, children Jake, seven, Elle-May, four - and 17 Sphynx cats.
It all started for Kelly at a cat show four years ago.
'I was with my grandma - we went past a pen and they had five pink, wrinkly babies in there and it was just like falling in love. I had to have one.'
So she did, albeit after a wait - they cost £1,000-a-piece and talking round husband Toby took a while.
Today, she has eight adults and nine kittens and the top floor of their three-bedroom home has been turned over to cats.
'There are three different rooms because they can't all mix - so there's one for the girls, one for the stud boy, because he sprays a lot . . .' And a third for communal use, with a teeny brass four-poster bed with a leopard-print cover and cuddly toys.
'I won the bed at a cat show. But it's a shame, because they don't like sleeping in it. They usually end up snuggling in with us - they're like little hot water bottles.'
And while the Cockrells' cats are lucky to get a bath every couple of weeks, every Thursday is bath night chez Hampton.
'And every other day I give them a little strip wash with a warm flannel. If you don't wash them, they can really smell. And their bedding needs washing every day, particularly if you have kittens.'
Not forgetting all their outfits. Kelly's cats have quite a wardrobe - cat jumpers, teeny fleeces, pink hoodies. Once they're appropriately dressed, they go on the occasional outing.
'I'll take them out for a walk on a lead or in their cat buggy - they need the extra layers because they lose heat so quickly. And they love going out in the car and putting their heads out of the window.
'They are the most beautiful, amazingly loving cats I have ever known. They've changed my life for ever. And the odd thing is that I always thought I was more of a dog person.'
Back in Great Yarmouth, Jack and Phyllis aren't in favour of dressing up. 'We might pop them in a sleeve of an old fleece if they're cold, but to me, anything else is making the cat look a bit silly,' says Jack.
'It's not very dignified - a cat's a cat after all, not a designer toy.'
And with that, he gathers up Darcy - or is it Dixie, Roy Orbison or Willie Nelson? It's difficult to tell - and pops her, or him, in my arms.
'To me, their skin feels so warm and lovely, like a peach, or a deflated rubber balloon. What do you think?'
Well . . . Darcy/Dixie/Roy certainly feels soft and warm - a bit like a horse's muzzle, but it's all a bit odd, too. And the moment I loosen my grip, she/he's off in a flash, leaving me with a face full of hairless tail and musty odour.
So far, it's tricky to see the attraction. Or why are the owners - who are friendly and chatty and seem normal - so happy to act like the cats' slaves. Jack looks appalled at the thought.
'They just love to give back the love. I tell you, if I'd have known about them 30-odd years ago, I wouldn't have had my children.'
And then there are the shows. They may not have been recognised by GCCF until now, but other bodies, such as The International Cat Association, have been sponsoring Sphynx-friendly shows for a while.
'Phyllis and I love the shows. We go every month, all over - Newbury, Tyneside, Milton Keynes, you name it. If we can come away with eight or ten rosettes, then we're elated.'
There are no money prizes - 'just rosettes and points, and a lot of kudos - that's what it's all about'.
Which is why this week's decision is so important. While the American TICA has lots of competitions, it is the GCCF that runs the Supreme Cat Show - the feline equivalent of Crufts, this year on November 22 - the jewel in the crown of pedigree cat shows.
This lot could never be accused of not taking it seriously.
'I want to breed more and more, to progress with the Sphynx lines,' says Kelly.
With the Sphynx, the judges are looking for ear shape and set - ('large and open at the bottom and round at the top,' says Jack); the break between forehead and nose; the chin ('very important'); the number of wrinkles ('a wrinkly cat will do so much better'); and size ('they like a solid cat').
Pedigree cats are on the up generally and breeders take it all very seriously, so gene components can be mixed and matched to produce refinements.
Which leads to a darker note - according to one insider who'd rather not be named, the judges' tastes tend to push breeders towards extremes.
'The current favourite for the Sphynx seems to be a shorter face, which can result in breathing and sinus problems. At the moment, it's not dangerous, but if things keep going that way, it has the potential to be,' says Kelly.
There may be no cash prizes yet, but there's quite a bit of money involved. Mainly because of the huge demand.
So while kittens for pets fetch £1,000 a piece, a 'breeder' will go for up to £4,000.
Kelly has two litters under her belt already, a waiting list and will sell only to people she knows through her Sphynx contacts.
Many of the Cockrells' customers are from overseas.
'We've sent them to Portugal, America, Australia,' says Phyllis. 'The air fare to the U.S. for the cat was £500 - we both could have gone for that.'
'But we don't do holidays anymore,' says Jack.
And what do their families think of it all? 'My children tolerate them, just,' says Jack. 'The grandchildren love them.'
Meanwhile, I am trying hard to like the Sphynx cat, but I am failing miserably. It doesn't help that there are so many of them hovering about in one small, hot bungalow.
As I take one last look at their strange faces and huge eyes, I am quite sure that, unlike Kelly, I'm going to stick to dogs.
