A strike could cause chaos for millions of travellers
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Tube drivers may join other London Underground (LU) workers in a 24-hour walkout planned for election day.
The Rail Maritime and Transport union are planning to strike next Thursday in protest at a 3% pay offer.
Drivers' union Aslef has warned it may ballot members on industrial action for a claim over a "substantial" pay rise.
A joint strike by the two unions would bring the transport system to a standstill and talks aimed at averting the walkout are continuing.
The RMT announced the strike on Wednesday after members voted in favour of industrial action by 2,614 to 643.
'Constructive' talks
As well as the pay rise, the RMT is seeking a cut in working hours to 32 per week.
A strike by thousands of signallers, maintenance and station staff and some drivers belonging to the RMT would cause severe disruption on the Tube, which is used by three million people every day.
It could also cause havoc for those attempting to vote in the mayoral, London Assembly and European Parliament elections.
LU described talks with the RMT on Thursday as being "constructive and amicable".
But Tim O'Toole, from LU, warned that financial constraints meant that changes needed to be self-financing as far as possible and must not lead to higher fares.