LU bosses challenged the validity of the strike, called by the Aslef union's leadership over its claims for additional Boxing Day pay, at a High Court hearing in London before Mr Justice Eder.
The union announced last week that it was calling four 24-hour strikes in the coming weeks, claiming LU was offering no extra pay for working the bank holiday.
LU said Aslef was seeking triple pay and an extra day off for working on Boxing Day, adding that the drivers already earned a premium in their annual salary for working on public holidays.
Bruce Carr QC, for LU, told the judge in a written argument that Underground bosses wanted an "interim injunction" to stop the strike.
He said Aslef had called the strike in breach of trade union legislation by balloting members not rostered to work on Boxing Day.
And he said industrial action would cause "substantial inconvenience" to travellers, shops and businesses.
Mr Carr added: "In short, (Aslef) included in the balloting constituency a significant majority of its members who could not in due course be called on to take strike action on 26 December 2011 as they were not rostered to work on that day."
He suggested that Aslef had "secured a false mandate by extending the right to vote to around 75% of members who it could not reasonably have believed would be called on to take part in the industrial action".
Mr Carr argued that there was "little likelihood" of Aslef succeeding at any trial.
But he said an injunction was needed because damages would "plainly not be an adequate remedy" for LU.
"The balance of convenience is overwhelmingly in favour of (LU) which faces losses as a result of the proposed unlawful industrial action," said Mr Carr.
"There is, in addition, the consequence of substantial inconvenience to the travelling public and to the shops and businesses which depend on a Boxing Day service being provided."
In written arguments given to the judge, Aslef said London Underground (LU) was applying to "injunct" strikes called between Boxing Day and February 13 2012. The union said the injunction should be refused.
Oliver Segal QC, for Aslef, said strikes had been called in relation to an industrial dispute over the terms on which drivers were required to work on Boxing Days.
"The dispute is long-running and similar industrial action was taken last year," said Mr Segal.
"The present industrial action was called following a ballot of Aslef's train and instructor operator members working for LU, around half of whom returned ballot papers, of whom 92% voted in favour of the strike action called for."
Mr Segal said LU had raised "several, generally novel, challenges" to the calling of industrial action.
He said: "Indeed, to the best of the knowledge of counsel instructed by Aslef, the arguments raised by LU on this application, which would have general though not universal application if correct, have never been raised, let alone upheld, before."
Mr Segal said it was being argued that a union should only ballot members rostered to work on intended strike days and should not ballot anyone on long-term sick or maternity leave.
He said LU's arguments were "misconceived".
"London Underground confuses 'strike' (in the narrow sense of: not attend for a rostered shift) with 'taking part in a strike' in the wider sense as understood both industrially and by the courts," said Mr Segal.
"That concept is not limited only to employees who are 'on strike' in the sense that they are rostered to work at the relevant time and do not attend for work but includes all employees who associate themselves with the strike with a view to furthering its aims, for instance, by agreeing in solidarity not to cover for rostered workers or supporting the strike by attending a picket line or refusing to cross a picket line."
He added: "Aslef wants, and will seek to persuade, all of its balloted members to associate themselves with the aims of the strike and to take part in it in that wider sense, including, in particular, by persuading all drivers (whether rostered or not) to support the 'concerted stoppage of work' by not covering for rostered colleagues and by attending on picket lines (as happened in 2010).
"Indeed, if LU were right in this case, it would produce the extraordinary result that Aslef would have 2,000 members directly affected by and with the same interest in the relevant dispute ... yet would have to ballot only 30% of them to establish the level of support for industrial action."
He said Aslef was "likely to succeed" at any trial of the issues before the court and called on the judge to refuse to halt strike action by imposing an injunction.
PA
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