I have this situation, although not as pronounced as my parents are in the U.K., albeit at a distance.
If you are offering your own room to them - you are doing more than enough. If they don’t like change - well, that’s a shame.
Don’t spend hours consulting them or negotiating with them. It gives them the impression it’s up to them. This is your home. You are entitled to live in it as you please, you live there 52 weeks of the year, you need it to suit you for the 46 weeks or so you’re there without them.
Decide what would suit you best, and whether it’s manageable for them. Obviously if an air bed or sofa bed wouldn’t suit them - no problem. They can stay in your room. That is a manageable option for them. It might not be their preferred option but it is perfectly reasonable - more than reasonable.
We had this with my parents. First time round we got rid of the spare bed too early on in hindsight. They slept on the sofa bed or hinted heavily for us to give up our bed for them.
Second time round (different house), we maintained the spare room as we needed it for ourselves. But now we need it for one of our kids to have a bigger bedroom. We would happily give up our room for them - we have a sofa bed we can use - but they have decided we don’t have enough space to host them now and it’s easier for them if we stay with them.
I think I’ve seen previous posts of yours - are your parents the ones who ride roughshod over you when they visit and expect to sit around watching tv, refuse to walk on the beach, etc? (Sorry if I’ve got you confused with someone else.)
As melodramatic as it sounds, I would be prepared for this to affect your relationship - they won’t like it. But that’s their look-out, not yours.