The good news is that compact compressors have gotten pretty decent in recent years, and you've got solid options in that budget. Look at the Iwata Smart Jet or the newer Badger Patriot compressors - both are around that price point and sit on a desk without dominating it. They're roughly the size of a small toaster, maybe 8-10 inches wide. The Iwata runs quieter than most, which matters if your spare room is near living spaces. The Badger is slightly cheaper sometimes and honestly performs well for model work. Both use oil-free designs so you don't need to worry about maintenance being a nightmare.
One thing to keep in mind though - even "quiet" compressors still make noise, they're just quieter than the old tank units. You're looking at maybe 65-75 decibels, which is basically a conversation level. If that bothers you, consider getting some dampening foam or stashing it under the desk with some acoustic padding. Also check the airflow ratings; for Gundam models you don't need crazy CFM numbers - most of these compact ones put out 25-40 CFM which is plenty for detail work. The tank capacity is smaller so they cycle on and off more frequently, but honestly that's not a dealbreaker for hobby painting. Just don't expect it to run continuously for 8 hours straight.
Since you're in the UK, check out scale model retailers rather than general art supply sites - sometimes they've got better pricing on airbrush-specific equipment. Ebay's worth monitoring too since folks sell used setups pretty regularly, and you could save maybe 30-40 quid if you don't mind slight cosmetic wear.