LONDON, March 27 (Reuters) - Trade unions Unite and GMB said members working offshore in Britain's oil and gas industry had shown overwhelming support for industrial action over proposed changes to their terms and conditions in a consultative ballot which closed on Friday.

Unite's members covered by the Offshore Contractors' Agreement delivered a 93.5 percent vote in favour of proceeding to a strike ballot, increasing the likelihood of North Sea strike action for the first time in a generation, the union said.

GMB's members also voted "overwhelmingly" in favour of an official ballot for strike action over proposals from clients and contractors to change their conditions of employment, GMB said.

The vote came after talks between GMB and Unite and the Offshore Contractors' Association in February and March failed to make progress on rota changes, rates of pay, sick pay and holiday patterns, GMB said.

"The vote quite clearly demonstrates the anger and frustration of our members employed in the offshore industry," said Dave Hulse, GMB National Officer. "Members are prepared to strongly oppose the changes from clients and contractors."

It was not immediately clear how many workers any eventual strike action would involve. The unions now face the task of putting together an electoral register that is robust enough to withstand any potential legal challenges, a process which could take some time, a spokesman for GMB said.

Some operators want to move to a three weeks on, three weeks off shift pattern, as opposed to the more traditional two weeks on, two or three weeks off.

Companies are also cutting headcount in their North Sea operations to trim costs, with hundreds of job losses announced at Royal Dutch Shell, BP, Talisman Sinopec, Chevron, ConocoPhillips and Taqa since oil prices plunged in 2014.

Unite Scottish Secretary Pat Rafferty said the "massive support" for industrial action should come as no surprise to offshore employers. "The industry agenda is clear in that it wants to impose a reduced number of employees to work longer and for much less -- it's a 'race to the bottom' disease that is unsustainable and unacceptable."

(Reporting by Claire Milhench; Editing by Janet Lawrence)