The challenge is being mounted by a Japanese group, which wants to turn the Thames site into a 600- bedroom hotel, conference and leisure complex.
Mr Justice Otton gave Shirayama, a Japanese hotel consortium, permission to make an urgent application for judicial review of the decision to delay the sale. The consortium accuses Michael Howard, Secretary of State for the Environment, of unlawfully using his powers for an improper purpose and of showing partiality towards the LSE.
The judge ruled, during a brief hearing at which neither the Government nor the LSE were represented, that there was an 'arguable case'. The full hearing is expected to take place next month.
In March, just before the general election, Shirayama agreed to buy Riverside building, the main building of five in the County Hall complex, from the London Residuary Body for pounds 60m, and made a down-payment of pounds 3m.
In July, the Environment Secretary issued a direction to the LRB under the 1985 Local Govenment Act not to take any steps in relation to the sale without first obtaining his consent. He indicated his purpose was to allow time for the LSE to submit a bid, even though the Government had earlier endorsed the Shirayama sale.
At the end of July, the LSE made an offer of pounds 65m for the entire site with a view to moving from its present buildings off the Aldwych to create a new European university for training senior administrators.
However, the LRB, set up to dispose of the disbanded Greater London Council's assets, said that the bid should be rejected in favour of the Japanese offer. It doubted the viability of the LSE proposals, which were conditional on the sale of its present premises.
The Japanese group is expected to argue that Mr Howard's direction was unfair as the LSE had been free to negotiate for the site at all material times, including before the Shirayama offer was accepted by the LRB.