That's why I'll think I should just take the case to court myself so that the judge can decide what is fair and reasonable compensation.
Going on what you've said already,
No receipt for the bike
Similar for the some of the items bought
No proof that it will cost 325GDP? or less to repair.
Were you seen by a doctor after the incident?
I'd say there's a chance that should you take it to court, that costs may not be awarded because procedure hasn't been followed. Each side pays their own. Go through the system in place and you'll not be facing this possibility.
Whilst the evidence required for a small claims court may be less than for higher court, you will be required to produce that evidence. This will include all communication sent, either they sent you or you sent to them. If you used the phone, you'll need times, dates and names. e-mail, copies of those.
You'll be representing yourself against someone trained in the system and familiar with it. Read back through both threads, and see how much of a disadvantage you're at already.
You were given a link by Arjimlad, my advice is to use it.