There is no point in initiating court action unless there is at least a fighting chance of winning it.
Unfortunately, court cases like this are not won or lost on truth and facts. They turn on which side has the most credibility, and I'm afraid that Pete's credibility is going to be damaged by the early problems and the gas safe report. It doesn't matter what we think, all that matters is what a small claims court judge thinks.
Although I think its wrong, I reckon the best thing to do here is to let it go. You could spend hundreds of hours chasing this, and may well lose. Even if you win, they will plead poverty and you will get £2 per week.
I had a situation recently where several £k turned on whether a landlord had given me notice of a rent increase.
He had sent it recorded delivery, which counted as proof of postage. This was deemed to count as "service of notice" even though the post office tracking system did not show delivery, and recorded that the letter was returned to sender as undeliverable. Whats more, the landlord freely acknowledged that he had received a letter from me which made it clear that I had never received it.
So even though I could prove that I had never received it, the law treated it as if it was delivered. After spending several more £k on legal fees, eventually I had to give it up. It doesn't make it right, but it was in danger of taking over my life, to the detriment of the rest of the business and my life.
Sometime, you just have to let it go, and let Karma do its thing on your behalf.