May Putin
British Prime Minister Theresa May and Russian leader Vladimir Putin have both 'expressed dissatisfaction' at the current level of cooperation between the two countries Getty Images

Vladimir Putin has warned that Britain's ties with Russia are unlikely to improve unless Theresa May reviews the UK's close relationship with the US and embarks on a "more independent foreign policy".

The Russian president's remarks come ahead of a G20 Summit in China next week, where he is expected to have a meeting with the British prime minister. In addition to Putin, May will also hold private meetings with the leaders of the US, India and China, according to the BBC.

During the European Union (EU) referendum campaign, former Prime Minister David Cameron claimed that Putin and Islamic State (Isis) leader, Abu Bakr al-Baghdadi, "might be happy" if Britain voted to leave.

The claim was slammed by Putin, who called it a "flawed attempt to influence the public opinion" in Britain ahead of the crucial vote.

Speaking to Bloomberg in an interview in Vladivostok, located on Russia's Pacific coast, Putin acknowledged that relations between the two countries "haven't been the best lately."

"The UK's relations with Russia depend not on its presence or absence from the EU, but on its special relationship with the US," he said on Thursday (1 September). "If the British side thinks that there's a need for a dialogue in some areas, then we're ready, we aren't going to pout."

Last month, May spoke to Putin for the first time since she took office and the pair expressed dissatisfaction at the current state of relations between Russia and the UK. Both leaders vowed to improve ties, the Kremlin said.

Relations between the two nations have been strained due to a number of factors. Earlier this year, the Litvinenko inquiry found that the murder of former Russian spy Alexander Litvinenko in 2006 was "probably" approved by Putin. Other disputes include Russian support for the Assad regime in Syria and Moscow's annexation of Crimea in 2014, which drew international condemnation.