Did you record the marriage at the British Embassy in Thailand? You should do it also so that it's recognized in UK (Philippine recognition is not useful for a UK spouse visa, but it will be useful to amend your Filipino passport of course).
For the Filipino side story, the Philippines Embassy in Thailand should give you (or send you) the official receipt for the NSO recording and this will be the official document to use with the Philippines administration in waiting the full recording at NSO to be able to get a NSO Sepca copy of your marriage certificate (in more than 4 months for your case as stated by the Embassy).
