British voters are increasingly dissatisfied with Prime Minister Theresa May and her government, according to an opinion poll on Friday, with less than a third of respondents happy with May's leadership.

With just over eight months left until Britain is due to leave the European Union, there is little clarity about how trade will flow as May, who is grappling with a rebellion in her party, struggles to strike a deal with the bloc.

The July poll showed 30 percent were satisfied with her leadership, down from 35 percent in June, with the rating for her government even lower at 22 percent, down from 30 percent in June. The survey of 1,023 adults was conducted for the Evening Standard newspaper by Ipsos MORI between July 20 and 24. The same measure among Conservative voters showed a fall to 55 percent from 68 percent.

In the June 23, 2016 referendum, 17.4 million votes, or 51.9 percent of the votes cast, backed leaving the EU while 16.1 million votes, or 48.1 percent of votes cast, backed staying. Many opinion polls were wrong about the result.

May has repeatedly said Brexit will happen and has ruled out a rerun of the 2016 referendum, although French President Emmanuel Macron and billionaire investor George Soros have suggested that Britain could still change its mind. Two years on from the referendum, the YouGov poll showed that the views of most voters on whether to leave had not changed. In the event of a referendum on Britain's EU membership tomorrow, 45 per cent said that they would vote to remain, while 42 per cent would vote to leave, with four per cent saying that they would not vote and nine per cent saying they did not know, The Times said.