You don't have much of a budget. Trombones in that price range are going to be pretty beat-up or low quality or both.
You could probably find a Besson 2-20, Yamaha 352, or Conn Director near your price point. You could start by looking in the Classified Ads here. Some folks have inexpensive instruments for sale.
If you can add 100 - 200 quid to your budget you might be able to find better quality used instruments.
Bruce Guttman
Merrimack Valley Philharmonic Orchestra
"Almost Professional"
I‘ve bought and/or sold playable examples of the following in that price range, all decent solid horns:
Yamaha 354 (nice overall condition)
King 606 (ugly lacquer but more importantly played well and good slide)
Olds Special (cheap and cheerful, probably the worst of the bunch)
I also got a Bach Mercedes in that range but it needs a bit spending on the slide to get the best out of it which would take it out of budget, it has a great sound though.
You only need a bit of patience and luck!
I‘d agree with Bruce, £400 is a lot easier to work with than £200, especially if you want anything other than a small bore horn.
I picked up a 1950 Conn 4H for under $200 USD (I think it was $120) from either Facebook Marketplace or OfferUp. There was some serious corrosion on the bell rear rim that I got mostly cleaned up. There was another 4H for sale locally that was about the same price. I considered it, but the opinion here was that it would only fetch around $200 unless really nice. So there wasn't enough margin to bother with it.
The 4H is a nice instrument in my opinion. Bore is .485" ... so barely smaller than the common .500"
Shipping is a killer, so finding one local to you is key. Finding one from an individual will cut the price significantly.
At that budget, you don't have the luxury of being selective about brand or model. Your best bet is the classified ads for a used student horn in good condition. If you hold out for a specific maker and model at that price range, then it could be 10 or 20 years before you play the trombone again.
A pro quality horn at the price you want to pay will require a trip to the repair shop, so add another $200-300 or so to get it playable.