As for the background to the UK Embassy's comments, it is now on the record that the Thai military junta has made a point of singling out a British citizen of Thai heritage critical of the Thai monarchy, Chatwadee Amornpat - aka "London Rose" - for "special attention" and has made numerous completely baseless and false claims that they are "extraditing" Rose from the UK to Thailand.
There are also a number of videos posted online which appear to target Rose in a harassment campaign. After posting one such video, the person involved later posted an image of themselves holding £5000 in cash, which led to some speculation that the source of such funds may have been the Thai military junta seeking to extend an harassment campaign into order to shutdown dissent in the wider Thai diaspora.
Either way, the UK Embassy in Bangkok seem to have made their position very clear - they will not tolerate the Thai military junta seeking to extend their repression onto British territory. The Embassy said that -
The UK is committed to freedom of speech and defends the right of individuals to express their views without the threat of intimidation or harassment. We have discussed with the Ministry of Foreign Affairs in Bangkok and the Thai Embassy in London. We have made clear that we will not tolerate attempts to enforce Thai military decrees in the UK that are aimed at preventing freedom of expression.