May campaigned for Britain to stay in the European Union and there are hopes that this pro-EU position could help during talks between Britain and the EU on what form their new relationship will take. However, it is unknown when May, known as a pragmatist and respected as a competent and experienced politician, will trigger Article 50 of the Lisbon Treaty which sets in motion the process of withdrawal.
So far, there has been an impasse between the U.K. and EU over an exit. The U.K. wants to know what kind of post-EU membership deal is on offer before triggering Article 50 while EU leaders have refused to go into any kind of talks before the withdrawal process is formally started.
May has indicated that she could wait until next year before triggering Article 50, a move bound to anger EU leaders who have urged the U.K. to stop wasting time and prolonging uncertainty.
Moscovici reiterated on Monday that "reducing uncertainty is the best way for the U.K. and the EU altogether." The Brexit vote has already prompted the European Commission to revise down its preliminary estimates for growth in Britain and the euro zone this year.
"We expect the increased uncertainty to reduce U.K. GDP by 1 to 2.5 percentage points by 2017 compared to the baseline scenario of remaining (in the EU). In the 27 EU member states and in the euro area the impact could be between 0.2 and 0.5 percentage points," Moscovici said on Monday, a statement from the European Commission confirmed.
Moscovici told CNBC that the revisions were not a fait accompli but a first analysis of the current situation. "It is not a fatality, it can be combated (by) reducing uncertainty. I think the article 50 can be invoked (now)," he said. "We must be very adaptive to what happens."
Discussions over a new relationship between the U.K. and EU could take place once a new British prime minister was in place, he said. That will come sooner than expected with U.K. Home Secretary Theresa May expected to be prime minister by Wednesday evening.
A new leader was not expected to be announced until September but the leadership race came to an abrupt end on Monday after May's rival for the post, Energy Minister Andrea Leadsom, pulled out, leaving May as the only candidate.
Portugal's Finance Minister Mario Centeno also told CNBC on Monday that the political transition happening in the U.K. was a positive step.
"You can start building upon that," he said. "Brexit is a structural change for Europe. And as any structural change, it needs a time period which given the size of the structural change needs to be large enough and long enough so that we can adjust. And we need to act fast. So yes in that respect the nomination of Theresa may maybe good news for the process itself."
—With contribution from CNBC's Katy Barnato. Follow CNBC International on Twitter and Facebook.