By Richard Lough

LONDON (Reuters) - Alain Juppe, the frontrunner to become France's president in next year's election, offered Britain hope on Monday that it could negotiate over the thorny issue of free movement of people under a new post-Brexit deal with the bloc.

On a visit to London, the centre-right former prime minister also said the border between the two countries should be moved back onto British soil - a foray into the controversy over how to deal with migrants camped at the French port of Calais once Britain has quit the EU.

Since Britons voted in a June 23 referendum to leave, European leaders have insisted it must continue to accept the free movement of workers if it wants to enjoy continued access to the EU's single market.

"We have to be open to negotiation on this point," Juppe told a news conference. "There are several possibilities."

Concern about immigration was among the main reasons Britons voted to leave the EU. British politicians who campaigned for Brexit have said they expect to be able to secure a favourable new trade arrangement without having to accept free movement.

Juppe, who is seeking his party's nomination in November primaries before the 2017 presidential election, said the bilateral Le Touquet accord that allows French customs officials to work on British soil and vice versa should be renegotiated.

"These agreements do not work," he said. "This should be done in Britain. I want those agreements to be renegotiated," he said, adding that with Brexit that situation was not acceptable for France anymore.

Juppe's comments were at odds with the line taken by Socialist President Francois Hollande, who has said the border agreement would not be affected by Brexit.

The Calais camp that has grown up in the past two years as thousands of migrants seek to avoid border controls there and to reach Britain illegally through the Channel Tunnel is politically controversial on both sides of the Channel.

Images of people desperately trying to leap onto trucks bound for Britain roused anti-immigration worries in Britain before the Brexit vote. The camp is also unpopular with local Calais businesses.

(Writing by Andrew Callus and Ingrid Melander; Editing by Gareth Jones)