The supermarket is seeking an injunction on the grounds that there are flaws in the balloting process used by the GMB union, with people who don't work for Asda being sent voting papers.
An Asda spokeswoman said: 'We've tried raising this with the union but they've ignored us - instead they've gone ahead and called a strike regardless. With only 1 per cent of our colleagues voting for a strike, we've got to do all we can to protect the other 99 per cent. The GMB has left us with no choice but to take legal action to try and put a stop to this.'
The GMB said its members working at Asda distribution centres voted three to one in favour of strike action last Wednesday (June 21). A union spokeswoman said it would 'vigorously' defend the action.
The union is demanding that national bargaining structures be put in place to cover pay, conditions and union facilities at the depots. It is also insisting that Asda pay staff an unpaid 2005 bonus of£300 per worker.
GMB members are due to walk out of 20 distribution centres from one minute past midnight on June 30 to 11.59pm on July 4.