RMT leader Bob Crow is undeterred and said "Despite this legal challenge, the 48-hour strike remains on.
"RMT will defend its position in the court against this latest attempt by an employer to use the full force of the anti-trade union laws to override a perfectly bona fide ballot."
The RMT claims TfL has failed to give its members assurances on jobs, pay and conditions once it takes over the Tube Lines contract. However, a TfL spokesman said: ‘This is an existing dispute about pay and conditions and not about the proposed transfer of Tube Lines to TfL.'
In the meantime, a planned 72-hour strike by RMT members on the DLR from 4am today was called off following a new pay offer.
Watch out for news reports on the result of the court action later today. However, even if the strike takes place, London Underground states it "intends to operate a full service to customers across the whole of the network, including on the Jubilee, Northern and Piccadilly lines, throughout the duration of the strike and all stations will remain open."
Update - The Tube strike remains in place as the High Court refused to grant an injunction to prevent the stoppage. Mr Justice Tugendhat said he had reached a "clear view" that he should not grant an injunction but gave no immediate reasons for his decision.
Bob Crow, said: "This is a massive victory, not only for the RMT and our members, but for every group of workers who stand and fight against job cuts and attacks on working conditions.
"The strike goes ahead and will be solidly supported. We expect major disruption across the network."
However, they will all be returning to court on July 9 for a one-day hearing to fully consider whether to grant an injunction ahead of the next planned strike on July 14.
TfL are still confident in running a full service between this evening and Friday 7pm, and said "The action does not involve London Underground employees, including station workers and Tube drivers".