By Francesco Guarascio

BRUSSELS (Reuters) - Britain will have to contribute to the European Union budget to access the internal market after leaving the bloc and will not be able to cherry pick benefits, a vice president of the EU executive said on Thursday.

Valdis Dombrovskis, who is in charge of the euro at the European Commission, also said the euro zone would weather any fall-out from Britain's vote last week to quit the EU.

Access to the EU internal market comes with conditions. "There will not be a possibility to have cherry-picking" for Britain, he said at a conference in Brussels, reaffirming comments by EU leaders, including German Chancellor Angela Merkel.

Some UK politicians who advocated a Brexit have suggested Britain could have full EU market access, including for the vital financial sector, and curb immigration.

But Dombrovskis said access "comes with the respect of the four freedoms, including the free movement of labor. It comes with financial contributions to the EU, and it comes with the respect and implementation of the EU legal framework".

He said the Commission was working with the European Central Bank (ECB) and other financial authorities to respond to any market volatility triggered by Brexit in coming weeks and months.

Despite initial panic in financial markets, Dombrovskis said the long-term effects would only become clear later and it was too early to predict the economic impact on the euro zone.

He dismissed as premature estimates circulated by the ECB on Tuesday that revised slightly down the euro zone's growth forecasts in the coming three years.

Dombrovskis also said the single currency union would not add new members soon.

"There is not going to be euro area enlargement in the next at least three years," he said.

Britain is not a member of the 19-member single currency union. The EU will shrink to 27 countries when Britain leaves the bloc.

Dombrovskis will be responsible for financial services at the European Commission from mid-July after the resignation last week of the British commissioner Jonathan Hill following the referendum.

(Reporting by Francesco Guarascio; Editing by Alissa de Carbonnel and Susan Thomas)