By Huw Jones

LONDON (Reuters) - Britain should spell out what happens to financial rules as Brexit gets under way to help regulators do their job and avoid a "mess" in markets, a top watchdog said on Tuesday.

The comments from Andrew Bailey, chief executive of the Financial Conduct Authority, are the latest to highlight the tricky challenge Britain faces in forging a new trading relationship with the European Union in a clear and timely way.

Bailey said clarity on how Britain will exit the EU, what the new trading arrangements will be and how to get from one to the other would be helpful for regulators to do their job of keeping markets orderly.

"We need a greater amount of understanding on all three," Bailey told parliament's Treasury Select Committee.

"Our interest is that on the day after Brexit we have a rulebook that works. If we don't, then we are in a mess. Getting from here to there is not quite as straightforward as it is sometimes presented."

A lawyer for banks welcomed Bailey's call for clarity, as uncertainty forces lenders to consider shifting some or all London-based cross-border business to elsewhere in the EU.

"This uncertainty is corrosive, and having no visibility of the government’s goals beyond a meaningless ‘seeking the best outcome’ gives firms no alternative but to plan for the worst," said Simon Morris, a partner at CMS.

Britain should also have a say in the financial rules it applies, he said. "The UK, as a major financial center, in a sense there is a need for a commensurate degree of influence over standards," Bailey said.

British Prime Minister Theresa May has said there must be controls on EU migrants to the UK after Brexit, a step EU leaders have said rules out the possibility of banks in Britain being able to passport services across the bloc as they do now.

Another option would be for Brussels to deem Britain's financial rules "equivalent", meaning they are just as comprehensive as those in the EU so that banks in Britain can serve continental customers.

In practice, equivalence has meant that non-EU countries like Switzerland and Norway have to effectively cut and paste the bloc's rules into domestic law.

"A world in which we were a taker of standards would be very difficult," Bailey said.

"If this is going to be based on what I call a system of equivalence, you can imagine that happening, then the setting of the equivalence standards has to be something that the UK regulators can influence."

Equivalence with the EU could be made easier if strong standards were set at the global level for trickling down to the EU and individual countries, Bailey said.

Global norms have been set for bank capital for years, but rules for insurers and conduct at financial firms are less developed at the international level, he added.

(Reporting by Huw Jones; Editing by Mark Heinrich and Alexander Smith)