If there really was a contract he should sue HP to honor it, my understanding is in the UK loser pays legal fees, so if he's sure about contract law there's no downside (I would suggest double checking the law on this though).
The 20% off voucher is a slap in the face, though. I'd never come out of this situation and still buy a laptop from HP, so it's effectively nothing.
Interested to know if something similar exists in the UK?
Are you sure about that? The small claims FAQ [1] on the Texas State Law Library site says lawyers are allowed. It cites section 500.4 of the Texas Rules of Civil Procedure.
Looking at the Texas RCP, it looks like small claims is defined by rule 500.3, which among other things says small claims cases are governed by Rules 500-507, so 500.4 would apply as stated in the FAQ.
Most states actually allow attorneys in small claims court. But even in a state that doesn't allow attorneys it probably doesn't matter. That's because it is usually easy to appeal small claims decisions, so if you lose in small claims court but think you would have won if only you had had an attorney you can appeal. The appeal is heard in regular court.
That being said, yes it does: https://www.citizensadvice.org.uk/law-and-courts/legal-syste...
UK law for consumer goods and sales, I would say generally doesn't require the buyer to be an expert. Laptops are items that are frequently included in sales and clearance sales at 50% off or more do happen. £400 is still a normal price to pay for a laptop. So I'd say the buyer could reasonably expect a laptop discounted to £400 to be the correct price, therefore HP were unreasonable to try to blame the buyer.
Without reading the contract, we cannot know. But given that the context was constructed by HP, there are likely multiple legal escapes.