By Huw Jones

LONDON (Reuters) - European Union lawmakers said they would be "tough but fair" in negotiating trading terms for financial services with Britain after its decision to leave the bloc.

The City of London is on tenterhooks after last month's Brexit vote.

Banks in the "square mile" financial district worry they will be cut off from the bloc's single market, forcing them to set up shop in the EU with all the extra costs that would bring.

The European Parliament will help shape the EU's new trading terms with Britain, and on Wednesday its economic affairs committee bid farewell to Jonathan Hill, Britain's member of the European Commission, who was in charge of financial services.

Hill resigned after Britain voted to leave the EU.

"Try to explain to people in London that what we want is a constructive relationship. We will be obliged to be tough because of course the interests of our own people will be at stake in the discussion," said Sylvie Goulard, a French Liberal member of the committee.

"Help us to help you."

EU leaders have stressed that Britain must continue to allow the bloc's citizens to find work in the UK if it wants its banks to maintain full access to the single market. Backers of "Brexit" want the flow of people from the EU to be cut drastically or stopped.

"We have to be tough, we have to be clear and fair in equal rules and rights," said Sven Giegold, a German Green party member.

"When you want to be part of the common market, you have to apply all the rules, but in a tone of friendship."

EU financial centers such as Paris, Frankfurt and Milan are already looking at ways to exploit Britain's exit, such as being the new home for the EU's European Banking Authority, currently based in London.

Hill was "very disappointed" with the outcome of the UK referendum.

"I believed that Britain had a great role that it could have played in arguing for an outward looking, flexible, competitive free-trading Europe, but the British electorate took a different view," Hill said.

David Coburn, a British member from the UK Independence Party, a harsh critic of the EU, said Hill should respect the outcome of referendum.

"The British public have made a decision... and that's the way it is. Best of luck in your next job," Coburn said.

Hill agreed constructive relations would be needed.

"Those constructive relations are more likely to be built by people who listen to other people in Europe rather than insulting them," Hill said.

(Reporting by Huw Jones; editing by Adrian Croft)