Business leaders have urged Gordon Brown to give Crossrail the go-ahead on his first day as prime minister.
The rail link will stop at key central London stations
The high-speed rail link from Berkshire to Essex is vital to keep London ahead of rival cities, they said.
"If we do not invest in the future we will pay the price," said Mervyn Davies, chairman of international bank Standard Chartered.
A bill is going through Parliament to obtain the authority to build the £15bn Crossrail scheme.
Funding has yet to be secured for the scheme, which would stretch from Maidenhead in Berkshire via Heathrow airport to Shenfield, Essex, through tunnels beneath London.
The project would create an important communication link for the capital, Mr Davies said.
"London is doing well as a city and I think if you are going to compete with the leading cities and leading financial centres of the world you need good communication links," he said.
"That is why Crossrail is so important to the future of London."
Mr Davies added: "There is no doubt that if we do not have it, we will have future problems."
The scheme is also backed by trade union leaders and London mayor Ken Livingstone, who estimated it would benefit the UK economy by £30bn if it became operational in 2015 as planned.
Mr Livingstone has described Crossrail as "even more important to London's long-term prosperity than our victory in winning the Olympic Games".