Thai police last week charged two migrant workers from Myanmar with the murder of David Miller, 24, and the rape and murder of Hannah Witheridge, 23, after the tourists' battered bodies were found on Koh Tao on September 15.
Junior foreign minister Hugo Swire summoned Thai charge d'affaires Nadhavathna Krishnamra and "stressed that there was a real concern in the UK about how the investigation has been handled by the Thai authorities," the Foreign Office said in a statement.
He also noted "his concern about the way that the police had engaged with the media on the case, and reiterated that the UK police stood ready to assist with the investigation and subsequent legal process", it said.
Swire emphasised the need for the British government and the victims' families to receive regular updates on the investigation's progress.
Thai police said on Friday that the two suspects had confessed to the crime and their DNA matched with samples taken from Witheridge's body.
There have been reports that the suspects were tortured into confessing -- an allegation Thailand has strongly denied.
The grisly murders delivered a fresh blow to Thailand's image as a tourist haven after months of political protests that ended in May's army coup.
