You don’t need to show any length of time for the money,just that you have it in your account.
The letter needs to be letter headed by your company and signed by them saying you are a remote worker and addressed to the Thai embassy in London, also they are likely to want to see your contract. They will want to confirm you have an address in the uk, I used my driving licence for this and was successful
but if I register and get a letter from them I’m hoping this might help to obtain a bank account and driving license, I’m a regular visitor to Thailand but now looking long term and new to this sort of legislation
Email them and they will reply promptly, probably better off asking your questions on here as you will get a more thorough reply as I’ve learned from experience