South West Trains says the tickets will be the cheapest in decades

Customers who book in advance will be able to buy �1 tickets for single off-peak journeys on routes between London, Portsmouth and Southampton.

The budget rail project, being piloted by parent company Stagecoach, could be extended if it proves successful.

High fares were deterring many people from taking the train, the firm said.

Big discounts

More than 3,000 substantially discounted tickets will be available every week on services starting from November 14.

The cheapest tickets will be sold for �1, while the majority of single fares will be available for less than �10.

If you can offer prices starting from a pound, it is within the budget of absolutely everyone South West Trains spokesman

Customers booking well in advance and using certain services will be able to buy a return ticket for just �2.

The offer - which began on Monday - is only available to people booking via a special website or by phone.

No discounted tickets will be sold at stations and the offer will not be valid on Sundays.

Untapped market

"If you can offer prices starting from a pound, it is within the budget of absolutely everyone," a South West Trains spokesman said.

"We feel that there is an untapped market with which we can fill the capacity of the rail market at these times."

The megatrain.com scheme is modelled on a successful budget bus service launched by Stagecoach in 2003.

More than 1.5 million passengers travelled on cheap megabus.com services last year, which operate between 35 cities.