they checked and said I had none and there was nothing more they could do
Barclaycard then wrote to me saying they’d made a mistake
They closed the case and accepted defeat, so they ended the contract. However, why did BC write to you directly and not to the company whom you'd already nominated as your agent for the claim? Was it the fact that the PPI company had already asked that caused BC to subsequently re-check or would they have contacted you regardless?
Also, I hate to say, but if they do end up getting the 25% that they believe they're entitled to, it will actually cost you 30% of the total, as their fee will attract VAT. Technically, you also have to pay tax on the 8% statutory interest on the compensation that you receive (which usually comprises most of the actual settlement), and this might be taken off by the bank automatically, but I think there's a form you can fill in to declare it/reclaim it as the vast majority of people will be covered by their individual interest-on-savings tax-free allowance.
I really don't know why companies like this are allowed to operate within the law. They shut down the scam companies that used to buy adverts on Google so that they would appear at the top when people searched for 'UK passport application' or 'Driving licence' or similar. They added no value and offered no tangible level of service as they just essentially copied and pasted your info 'on your behalf' on the same proper government website that you could have used yourself and then whacked their extra fee on top of the actual official cost.
These PPI companies are doing nothing that you couldn't do yourself (maybe with a little free online guidance from MSE or the FCA). They try and scare you with tales of 'ooh, just think of all the forms you have to fill in', but these are mostly just simple details such as your name, address, employment history etc that you would have to tell the companies in the first place anyway. It's not like they're conveyancing solicitors guiding you professionally through the complex laws and procedures when you buy a house - it's literally just 'copy, paste, send to every single bank, send a standard claim template in to any positive answers, get the money, keep a massive stack of it and pass the rest on to the rightful claimant'.
The banks did sometimes fight back at first, but now they've mainly sucked it up and are just taking the hit until the end of August. As they have to pay 8% interest, if they realise that you're on the case in claiming, their losses are minimised the sooner they settle. Some banks have actually contacted customers out of the blue to say 'sorry, you may have heard that we ripped you off - here's a cheque for what we owe you including interest'.
It's a shame that people who don't claim before the deadline for whatever reason might miss out on their rightful compensation, but it will be such a breath of fresh air not to have to keep seeing and hearing that annoying shouty man from GB in every ad break. Charlatans, the lot of them.