All trains on the London Underground should be driverless, according to the Conservative group on the London Assembly.
In a proposal to the mayor, the Tories claim it would save about £141m-a-year in wages and prevent strike action.
Transport for London (TfL) said staff on board trains reassure passengers, provide information and help with speedy alighting.
The Rail, Maritime and Transport union said the proposal would hit safety.
In a memo, seen by BBC London, to the London Mayor Boris Johnson, the London Assembly Conservatives say: "Driverless trains offer a safer, faster, more efficient level of service," the memo states.
"Such a system would end the strangle-hold militant unions have on the city's tube network and seriously curtail their ability to bring London to a standstill.
"The Victoria and Central lines already use technology which has reduced train drivers to door openers.
"Current upgrade work will extend this to the Jubilee, Northern, Piccadilly, District, Circle, Hammersmith and City and Metropolitan Lines.
"With the recent decision to bring [maintenance company] Tube Lines under the control of Transport for London, this is the time to switch to a completely driverless train network."
It adds that a driverless network would solve the "poor state of industrial relations between London Underground management and train operators."
It said between 31 December 2005 and 23 December 2009, there were 20 days of strikes and between the 21 April 2005 and 23 December 2009, there were 34 strike ballots involving the RMT and other unions.
But Bob Crow, general Secretary of the Rail, Maritime and Transport union - the biggest union on the Underground - said: "It is badly thought out, safety has not been thought out.
"What will happen in a terrorist attack, a derailment or a massive signal failure, is you could have 600 or 700 people trapped down the Tube with no driver - there would be utmost panic.
"I don't think the travelling public will put up with that.
"Under normal circumstances I would be tempted to dismiss this leaked report as some kind of a joke, cooked up by anti-union fantasists, but in the current climate of cuts and attacks on public services we are taking it very seriously and it will be resisted.
"It may well be that some junior politician is simply flying a kite to make a name for themselves, but RMT will not sit back and allow this lethal and unworkable idea to gain any traction whatsoever."
A TfL spokesman said: "The Victoria and Central line trains are the only ones currently in operation on the Tube network that are automatically operated, however on these lines a train operator is in the cab.
"Having a member of London Underground staff on a train helps give reassurance to passengers, ensures prompt opening and closing of doors, speedy boarding and alighting of passengers and departure of the train."