Russian President Vladimir Putin and British Prime Minister Theresa May held talks for the first time on September 5, with Moscow keen to improve ties.
Kremlin spokesman Dmitry Peskov told reporters that the meeting, on the margins of the G20 summit in the Chinese city of Hangzhou, was "good, constructive, and open."
"Mr. Putin gave a clear and unequivocal indication that we are interested in completely reestablishing our relations and dialogue in all areas, including the most sensitive ones," he added.
Britain's relations with Russia have soured in recent years, especially over efforts to prosecute the case of Kremlin critic Aleksandr Litvinenko, who was murdered by poisoning in London.
Britain has also been one of the most fervent supporters of Western sanctions against Moscow over Russia's aggression in Ukraine.
Observers have said that Britain’s vote to leave the European Union could play into Putin's hands as he has been accused of trying to drive a wedge between EU members.
Based on reporting by AFP and AP