Look on the web for details of what the letter before action should say, and send that. Basically it is the ‘official sounding letter ‘ you describe, but is something you have to do before doing the small claims process. If you send that then it saves you wasting ages for them to do nothing. All you have to do is put the right wording in your letter and you save yourself time and demonstrate to them that you’re serious, not some sucker who will just waste their time writing pointless letters forever.
Search for DIY justice I think it is called , they have a great guide to small claims process.
Don’t waste time over anything, do everything as quick as possible, bang on the minimum times, like if you psend a 14 days or i’ll go to court letter, get the court action in on day 15, then assuming you go to court, apply for default judgement first thing on the allowed day, and the day you get a court judgement instruct high court enforcement (you can do that for debts of that size once you have a small claims judgement ).
Don’t piss around giving them tons of final chances and more time, they obviously aren’t going to pay without going to court, and if it goes to court they pay your costs. The longer you wait, the more likely they go bankrupt or whatever, and your money is lost.