Stephen Ashton's MP Richard Ottaway said he had been in touch with the Foreign Office to check that everything was being done to support the investigation.
The MP, who chairs the Foreign Affairs Select Committee, has also contacted the family to extend his condolences and offer any help that he can.
The UK ambassador to Thailand will be visiting the scene of the crime tomorrow.
I have written to Mr Ashton's family to offer my help in any way that I can.
I am determined to ensure that justice is served and that whoever is responsible for this heinous act is held to account.
I understand that under Thai law the authorities have up to 84 days to bring charges and there is a bit of a history of this time being taken in other cases.
It may be some weeks before charges are finally brought.
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TV favourite Cilla Black, who has died aged 72, gave viewers a "lorra, lorra laughs" during her long career.
Some rain in the north. Very warm sunshine in the south
Blind Date and Surprise Surprise star Cilla Black,72, has died, according to reports.