The European Court of Justice (ECJ) will decide whether the retailer can offset £30m tax losses in France and Germany against profits made here.
Should it be permitted to do so, the floodgates would open for other British companies to follow suit.
The mobile phone retailer Carphone Warehouse, First Choice holidays and BT are among an estimated 200 firms that have already lodged claims against the Exchequer.
Hartley Foster, the head of tax litigation at the law firm DLA Piper, said: "Any multinational that has losses arising in any of its European operations is a potential claimant." Vodafone alone may be in line for as much as £7bn.
Tax experts expect the ECJ to find in favour of M&S, but said the Chancellor's ultimate liability hinged on how far the Court wanted to harmonise European tax laws.
"There is not much Europe-wide co-operation on how to change tax systems across the Continent, but M&S could change that," Mr Foster added.
At the moment, UK companies can only use losses racked up by a subsidiary to reduce the amount of tax it has to pay if that subsidiary is based at home.
In April, Miguel Poiares Maduro, an advocate-general at the ECJ, said that a British law barring M&S from offsetting tax losses made by continental subsidiaries against its UK tax bill violated European law.
Tax experts said they were "75 per cent" confident that the ECJ would back M&S. The retailer declined to comment. Chris Morgan, the head of KPMG's EU tax group, said: "Any rules that apply differently to a cross-border investment are contrary to the idea of a single market."
A Europe-wide tax shake-up could see member states introduce a system to provide for cross-border tax loss relief.
Mr Morgan warned that governments would need to be careful that any new laws did not allow companies to use losses amassed in one country twice. "Governments will need to negotiate to make sure their rules are compatible," he said. "We need reciprocal rules, otherwise the UK Exchequer will be subsidising investment outside the UK."
Less expensive variants of the ECJ's decision for Mr Brown could see the court declare the UK's corporate tax structure illegal but give the country a period of grace to change its tax relief system, making retrospective claims impossible.
The court could also rule that only companies that have already lodged claims should benefit from the ruling. Pilkington, InterContinental Hotels, Portakabin, Chubb and Asda are among those with outstanding claims.
M&S lodged its claim through its regular tax return process five years ago. The British courts referred the case to the European courts in 2003. The retailer has since sold its operations in continental Europe.