In initial deals, the British capital's benchmark FTSE 100 index gained just 0.1 percent to 7,695.37 points compared with Monday's closing.

In the eurozone, Frankfurt's DAX 30 won 0.3 percent to 12,580.31 points and the Paris CAC 40 added 0.2 percent to 5,410.19.

The pound meanwhile held steady after tumbling Monday following British Foreign Secretary Boris Johnson's angry resignation over a post-Brexit agreement.

Pro-Brexit minister Johnson has long been seen as a thorn in May's side, and analysts say his resignation increases the chances she will face a possible leadership challenge.

That would throw Britain into fresh turmoil -- and the possibility of another general election.

In the run-up to the nation's shock Brexit referendum in June 2016, Johnson was a prominent Leave supporter but Theresa May had backed the unsuccessful Remain campaign.

"Pound stabilises as May remains and Boris leaves," noted London Capital Group analyst Jasper Lawler on Tuesday.

"Theresa May defiantly stood her ground on Monday; with threats of a vote of no confidence unfounded, she lives to fight another day as prime minister.

"As Theresa May's position stabilised, the pound managed to pick itself up."

Johnson's resignation on Monday came hours after David Davis, London's point man on Brexit talks with Brussels, also stepped down over the agreement.