Mr Cameron, as revealed at a St David's Day reception this year, is one of the television show's biggest fans.
The Camerons will want to book immediately, then, for the family comedy Nativity 2: Danger In The Manger!, which stars Stacey herself, aka the actor Joanna Page. Mr Cameron was so thrilled to meet his comedy idol at the No 10 reception that he gave her a Wayne's World-style "we're not worthy" bow.
"He said he was a massive fan of the show, absolutely loved it, knew all the catchphrases and asked if it was going to come back, the same as anybody who watches it," says Page.
So, is it coming back? "At the moment I'd say it's not. In every series we filmed we always had an inkling that they'd write more and it would be coming back. But for the last one, the third one, it was a dead-set 'no, that is it, the end'. So we were all really sad when it finished because it really was a goodbye."
On to bigger, and bumpier, things. Nativity 2, a follow-up to Debbie Isitt's 2009 hit, finds us back at the first film's West Midlands primary as it prepares to enter the annual Song For Christmas choir competition. There's a new teacher in town, – David Tennant, the former Doctor Who – and his wife, played by Page, is pregnant. Page wasn't in the nativity way when they were filming, but she is now. She and her husband, fellow actor James Thornton, are expecting their first child next year.
Nativity 2 allowed her to get in some practice with a bump. "It was just really comforting. I wouldn't take it off all day. I'd sit there and have my lunch with it still on. I'd probably be still be wearing it now if I was allowed to. But now I've got my own bump. It's heavier and moves, so slightly different to my prosthetic one," she laughs. That wasn't the only advantage: she kept some of the costume, complete with elasticated waistband, and wears it now.
Having Tennant as a screen husband was another cosy fit. "He's great: really dry, witty, made me laugh a lot, but also he's such a brilliant actor you feel really safe and secure with him. You just know he's going to be able to improvise well and come up with really good stuff."
In a straight contest between Tennant's Mr Peterson and Gavin & Stacey's Mathew Horne, who would win? "They've both got their lovely qualities," is the 34-year-old's diplomatic reply. "I've been very lucky with all the leading men I've worked with. I don't think I could choose between them."
Born in Swansea, Page trained at RADA in London before going on to work in the theatre, television and several films, including Love Actually. Gavin And Stacey came along in 2007 and changed everything. She knew from a first read of the script that she wanted to be in it, but had no inkling how much of a talking point it was to become.
"We sort of knew there was some magic between us all and we all gelled, got on really well and were having a great time. I didn't really have any idea it was going to be as big as it was. It was only when we started filming the second series when we started getting nominated for things. It was a really mad time."
She still gets recognised wherever she goes, and due to the power of repeats that won't change any time soon. "In everybody's eyes I'm still going to be this really young 20-year-old, which is fine by me."
Page is Welsh and proud of it, but like some of her fellow countrymen she has come under pressure to lose her accent to get jobs. Rhys Ifans has spoken of the same happening to him.
"When I came out of RADA, nobody wanted a Welsh accent," says Page. "I've been Liverpudlian, northern, Scottish – everything apart from Welsh. I'd go up for an audition and they'd say 'Any regional accent apart from Welsh?' I remember thinking there's been the Irish thing, the northern thing, the Scottish thing; when is it ever going to be the Welsh thing? It's never going to come."
But then Gavin And Stacey arrived. "It's now really cool to be Welsh. It feels amazing, being accepted, people loving your accent. Now when I go for auditions they'll go, 'Can you be Welshier?'"
While she's appearing in cinemas in Nativity 2, Page is also back on the small screen as the face of Superdrug. Mr Cameron, and everyone else, can now see her most evenings looking sickeningly well-organised for Christmas as she birls round the shop. Is she that well organised in reality? All family and friends presents are sorted, apparently. "They're all getting make-up," she laughs.
Come Christmas, she will be found in front of the fire, feet up, issuing orders. Nothing else, in the words of Stacey's best pal Nessa, will be occurring. Tidy, as a certain PM might say.
Nativity 2 opens tomorrow