I put this as a comment to a post a few minutes ago. On reflection it is so important to British passport holders wanting to renew/replace their passport it deserves a post of its own. 1. The British Embassy has nothing whatever to do with these matters. 2. VFS act as agents for His Majesty's Passport Office in Thailand. NOW THE IMPORTANT BIT: VFS ARE RUNNING DOWN THEIR Trendy Building HQ in BANGKOK (Sukhumvit Soi 13) where they have been forever and a day. You are still OK "ish" at Trendy Building to 18.3.24. From 24.3.24 address will be VFS Thailand, The Shoppes at Belle Grand Rama 9, 131/1, 141/1, Unit BS003-BS003/1, 1st Floor, Rama 9, Huay Kwang, Bangkok, 10310. The Chiang Mai VFS office motors on as before, in fact to my eye has longer hours. However though the costs have risen a lot there ie +GBP76.50 as against Bangkok. Wherever, it is needed to book an appointment. I'm guessing that may now be difficult (?) for Trendy Building at the moment.
TLDR : Answer Summary
The British Embassy is not involved in passport matters; VFS Thailand acts as agents for His Majesty's Passport Office. VFS will relocate from the Trendy Building in Sukhumvit Soi 13 by March 24, 2024, to their new address at The Shoppes at Belle Grand Rama 9. Appointments are necessary during this transition, which may pose challenges for users.