Unfortunately, once it starts bubbling there's nothing you can do but reupholster it; I suspect the cause is plastic that lacked the requisite "sunscreen" ingredients to resist attack from UV rays. I'd start by asking local auto detailing places, since they often have or know the people who fix leather and vinyl problems for local car dealerships.

 

Don't have a photo of my glovebox door, but it's pristine compared to the melted messes I've seen in other posts, very minor bubbling. I was researching ways to harden leather and vinyl, found a suggestion that Elmer's glue might work - I recovered my console lids last year and although that's leather (or synthetic leather), I decided to test various ways to harden the old piece I took off. Used Elmer's white glue, two types of rotted wood hardener, and a fabric stiffener - all fails except for the Elmer's glue - it was still a bit pliable but definitely stiffer than it was before treatment, matte finish too. I'm going to try painting the soft top half of the glovebox lid this week and see how it lasts. I already used a needle to stick a hole in each largish bubble (~3/16") then used a hard wallpaper roller to squeeze the air out and see if I could get the top layer of vinyl to stick to the stuff underneath - worked pretty well, most bubbles disappeared and since we haven't had a hot day since they're still flattened. Will report back in a few weeks/months with photos of how good the Elmer's worked out - I'm confident it will last, just need to keep the sun off the glovebox. After seeing the horrible melted photos of others when their RL was only 4-5 yrs old I wondered why mine was still almost perfect since I don't have a garage - by pure luck, where I park in my driveway a large maple tree shades the passenger side until noon, and after the sun passes over the car to the West sunlight never hits the passenger side, so my glovebox has basically been hidden from the sun for 20 yrs. Don't know why some people who said they garaged their RL had the same problem, must have been where they parked at work.

 

My Rejendo has a slight bubbling directly under the passenger air vent - it's so precise that I believe it's a combination of the heater air & sunlight.

Yes, the sun does shine in the UK. Sometimes...