I play a little melodeon; many of the same principles apply.
There's a lot that can go wrong with a bellows instrument over time. Reeds rust, bellows seals rot, joints seize up. None of this will happen if they are looked after or stored properly. All of it will happen if they're left in a damp cellar for 20 years.
Many parts of a bellows instrument can be replaced or repaired, but if you're balking at £500 for an instrument, you probably don't want to pay for professional maintenance. Compare it to a £200 entry-level guitar, which has much fewer moving parts, and much bigger economies of scale. Guitarists are spoilt when it comes to the availability of affordable instruments.
As a beginner, with any instrument, you should be less concerned with timbre, and most concerned with basic responsiveness. You'll be seriously held back if you try to learn on an instrument where the reeds respond unevenly, or there are some stuck keys. You'd be learning habits to compensate for the instrument's faults, that wouldn't be useful habits when you move to a better instrument.
For this reason, I think it would be a mistake to buy an accordion from eBay sight-unseen. Handle it before you buy it. When you take into account the travel costs this might entail, perhaps £500 will start to seem less expensive.
Just to add to your financial fears; I'd really really recommend some one-on-one lessons. You say you're not "musically talented". This means you're really going to struggle without the help of a teacher.
It might be a good idea, in fact, to find the teacher before you find the instrument. The teacher might be able to lend you an instrument or put you in touch with someone who can lend you one. Then you'd have a chance to find out if the accordion is really for you, and when you buy one, you'll have enough of the fundamentals to be able to tell a playable instrument from a dud.