I have spoken to a few companies who have said that our current model is now obsolete, so we can’t get it fixed.
Hrmph. If you can find an old school (old!) fitter, who's known Rayburns since the 60s and 70s, I bet they would know how to sort you out / source any bits you need.
We had an original 1950s "Pattern No. 1" Rayburn in our cottage in the late 1990s, got it completely refurbished, ran as good as new. (I realise this is now more than 20 years ago, but the device was over 40 years old at the time. The point is, not much breaks and much is standard, so someone who knows them of old would know what to get and how to adapt it if necessary, even if you can no longer order that specific part.)
The chap who fitted our new solid fuel Rayburn, 8 years ago in the farmhouse in Cumbria, is almost certainly retired now, I'm afraid. He wasn't a certified Rayburn fitter, but he'd done work for us before and we knew he was competent, professional and wouldn't cut any corners, so asked him if he could do it. He researched the specifics of Rayburns and arranged for the HETAS certification of his work. I wish you luck finding your very own "Hugh"!