The offer, made to the Strategic Rail Authority, would involve replacing most of SWT's rolling stock with new trains, extending Waterloo station to accommodate bigger or longer trains and rebuilding bridges and platforms across the network.
SWT is forecasting that passenger traffic will grow by at least 40 per cent over the next 10 years. Introducing double-decker trains would allow SWT to free up more capacity for mainline services while relieving overcrowding on its busiest suburban routes.
Mike Kinski, chief executive of Stagecoach, said that the company had already spoken to rolling stock manufacturers but no final decision had yet been taken on whether to proceed with an order.
SWT's existing seven-year franchise, which runs out in 2003, is due to be re-let in the first quarter of next year.
Double-decker trains are already in service in Amsterdam, Paris, Sweden and Germany. They are not built in the UK but Alstom, the Anglo-French group, has a factory in Portugal which makes them.
Mr Kinski also said Stagecoach was keen to bid for other inter-city and London commuter franchises. Stagecoach owns 49 per cent of Virgin Trains, which has already confirmed that it intends to bid for a 20-year franchise to take over the East Coast Mainline from the current operator, GNER.
Further details of the Virgin bid emerged yesterday. Virgin will offer to replace the entire fleet on the east coast line with 37 new high-speed tilting trains costing pounds 590m. It is also proposing to increase the speed of the trains to 140mph on the entire length of the route through a pounds 2bn upgrade programme carried out in conjunction with Railtrack.
Mr Kinski also announced plans for an increased pounds 5m marketing spend on the Internet rail booking service it owns jointly with Virgin, thetrainline.com. More than 300,000 people have registered with the company and the website is receiving 150,000 inquiries a week.
He was speaking as Stagecoach unveiled better than expected interim results with pre-tax, pre-exceptional profits up 34 per cent to pounds 130m for the six months to the end of October. Stagecoach shares closed 4 per cent higher at 168.5p.
Mr Kinski defended the controversial rights issue used to fund Stagecoach's $1bn acquisition of the US bus company Coach and said it intended using its pounds 400m war chest to expand further into the American bus market. Coach contributed pounds 34m to operating profits in the three months from August to October.