The RMT union said that it was holding a strike ballot "in response to London Underground riding roughshod over agreements and abusing a range of agreed policies and procedures".
They are unhappy with plans to split a depot in Acton Town into two - claiming that that tube bosses are "ripping up rosters and booking times" and "refusing perfectly reasonable requests for decent staff facilities".
RMT General Secretary Bob Crow said:
"Driver and instructor members on the Piccadilly Line are furious at this unilateral attack by the company on working conditions, agreements and procedures and we are moving forwards with plans for a ballot for strike action.
"We will of course be in talks with our sister drivers union ASLEF and London Underground should be in no doubt about the unions determination to protect working conditions and to stop the abuse of procedures."
RMT General secretary Bob Crow said: "One of the first things fascist dictators like Hitler, Mussolini and Pinochet did when they seized power was to ban transport workers from taking strike action so the Tory group on the London Assembly find themselves in some high profile company on this one.
"This crowd have obviously over-dosed on their post-Thatcher adulation and are looking to ramp up the anti-union rhetoric in advance of the publicly financed funeral on Wednesday.
"Of course, banning the fundamental human right to withdraw your labour, a right that distinguishes a free workforce from forced labour, is all the rage on the far right and anyone stupid enough to try and embark on such a policy is doomed to failure."
The Conservative report included an opinion poll, which found that 48% of Londoners support some kind of ban on strike action.
A complete ban - which would see workers sacked for withdrawing their labour - was backed by 16%.
Another 15% supported the introduction of rules used on the New York subway, which bansstrike action but give unions a right to binding arbitration. And a further 16% favoured pendulum arbitration in which a judge cannot compromise but has to choose between either the employers or unions position.
The survey also found that:
59% think it is too easy for Tube workers to go on strike.
Only 14% of Londoners back the status quo on strike law and 6% want to make it easier to strike.