The UK only issue ETDs (Emergency Travel Document) if you lose your passport and need to travel urgently. I would apply for the new one as quickly as possible, and you'll have to take the damaged one to Thai Immigration and see what they say.
I would. It took over 8 weeks to renew my son's passport. Once you submit the application it's sent to HMPO in Liverpool. Due to Christmas and Covid, I would think they are taking a while.
You fill in the form; photocopy all the pages of your damaged passport; complete the payment form; make an appointment at VFS/The Trendy (Sukhumvit soi 13); take it all to them.
I can only speak for my own case, but no they have never queried it or told me he needs to do it (he's 5 now, but has had an annual Extension since he was 1).