Eight workers were dismissed by the infrastructure company Metronet following the discovery of more than 100 empty beer cans and an empty brandy bottle in their mess room at Farringdon station. The men have protested their innocence, saying they knew nothing about the drinks.
The RMT said union members employed by Metronet on track and signal maintenance on the underground voted by 5 to 1 to support their sacked colleagues. No date has yet been set for industrial action, but the RMT executive is due to meet later today to consider its next step in the dispute.
Announcing the result of the strike ballot, Bob Crow, general secretary of the RMT, said: "All of the people who were sacked were tested and proved negative for alcohol. There is not a shred of evidence that says any of these men were guilty.
"Management should do the decent thing and stop conducting a witch hunt in which, if the witch drowns, she is not guilty and if she stays afloat she is a witch. Otherwise there will be serious disputation on Tube lines."
RMT London regional organiser Bobby Law said in a letter letter to Metronet that in 20 years as a union official he had never witnessed an "injustice on this scale".
Before going on to list "32 outstanding issues arising from the disciplinary process", Mr Law said: "Despite each accused member being forced to endure two 'fact finding' interviews, two disciplinary board hearings and one appeal board hearing, not a shred of evidence has been produced to prove that any of our members were consuming alcohol or that they could be linked in any way to the discovery of alcohol at Farringdon."
"You will be aware that the safety of the travelling public and our members is paramount to this union and we would not condone the use of either drink or drugs by staff while on duty.
"It is therefore essential that we have fair procedures that are fully complied with by all parties. In this instance it is clear that Metronet Rail has failed to do this." Mr Law accused Metronet of showing "total disregard" for its own disciplinary procedures.
Metronet insists the staff were fully aware that alcohol was being stored on the premises, against the company's "robust" policy. It has not accused the men of drinking but says they were aware alcohol was being stored against the rules. A statement from the company is expected later today.
London Underground said: "This is a dispute between Metronet and its maintenance workers. We will continue to look to our employees to do their jobs because the dispute is not with LU.'"
The Liberal Democrat London mayoral candidate, Simon Hughes, said: "This sort of industrial action does nobody in London any good. It is no good for the passenger, no good for London Underground and no good for the unions.
"In spite of today's ballot the union must think again and pull back from what will be yet another unpopular, unnecessary and unjustified strike."
The Tory mayoral candidate, Steve Norris, proposed a no-strike agreement on the Tube. He said: "I'll make the unions an offer they ought not to refuse. Tube strikes cause misery for passengers as well as damaging London's reputation and I am determined to put an end to them.
"I will get Bob Crow and other union representatives round the negotiating table to sort this problem out once and for all. No union should have the right to bring the city to a standstill."