David Cameron's brief statement yesterday (22 October) during Prime Minister's Question Time in the House of Commons (24:40 into the video). UK providing 'technical assistance' to Thai investigation.

Point really to note is that open questions will continue to be raised in the UK, and whilst there's obviously no way that UK police can be directly involved in the case, their eventual report will be made public, and potentially direct questions will be made in Parliament which must be responded to.