It's similar. Probably unlikely a court will have declared anyone incompetent, we save that tag for politicians, but you have a duty not to rip off people you should be able to tell aren't totally with it.

Coming at this from the other side, I'm usually the one stuck with goods, consider the following.

A paper contract is what you need. All is not lost if you don't have one though, just ask for a copy of their terms and conditions "for use when seeking advice". You can still dispute a paper contract though.

Negotiate. Ranting, wailing, threats, just shows the shiny suit double glazing sales types their bullying had an effect. They enjoy it and it drives what can be a psychotic need to win. Present them a deal they can "win". Just ask what they want in a calm, detailed way. Do not pretend to be anything you aren't, we salesman love a "not fit for purpose" line that the interweb claims is in the Sale of Goods Act 1884 to prove the whiney PITA customer doesn't have a Scooby.

Any contract, verbal or not has to be reasonable, legal, agreed. You are going to dispute it's reasonable. What work did they do for £1100? A bit of admin, bank fees maybe?. You are going to dispute that your brother agreed to the non-refundable part, at least on the second payment because he'd be stupid to pay two deposits when the first had secured the bike. Ask for details of what work they did for this money, they are claiming you paid for a service, so what was it?

Ask for contact details of the company directors, owners, who ever is higher in their chain of command. Ask who their lawyers are.

Tell them you are considering completing the contract and ask about delivery etc. Maybe they'd like to breach the contract because they've already sold the bike to another customer?

If lawyers get involved they will be the only winners. It's better to look like the customer who'll go away if he gets most of his money back, but does have the funds to bust the dealer if sufficiently riled.

Andy