Thanks for the replies folks...and thanks for the offer guhrillastile too...I'll let you get Christmas out of the way and see whether I've solved my problem in the meantime.
The bowl's metal collar is about 21.6mm wide on the outside, and measuring the hole inside which the stem should slot into gives me the 11.5mm at the wider end. So far in the UK I have only found one online place which I can source a Peterson stem from, but these are the larger 12-13mm items. They say that the smallest ones to fit my bowl are no longer available, and they don't have any new old stock. The larger stems are about £14 I think, with shipping on top of that. So I guess it would be possible then to buy one of these and then have it turned to reduce it to the right fit...I hadn't thought of that until you all suggested it! Great idea!!! Actually the online shop has also said that their repair guy can make and fit a stem up for £25 (including return shipping), but his waiting list is currently 6 - 8 weeks. I suspect slightly longer with the Christmas break approaching too.
My only local repair guy is still a yank to get to and didn't reply to the last request I sent (making and fitting a new bowl to a calabash), so I'm probably not going to try him for this if I can help it. I ended up sourcing a bowl and doing the fitting myself! Thus I'm left with either doing this myself (I don't have a lathe, so anything I do is going to have to be by hand...but I'm always happy to have a go!), finding someone else to alter a larger P-stem, or finding a stem which happens to fit of its own accord.