The support is critically-timed, given recent dissent from Tory backbenchers, with the government set to approve High Speed Two (HS2) when it publishes its response to a public consultation before Christmas.
Louise Ellman, the Labour chair of the committee, said the new line will eliminate concerns over a capacity squeeze on the west coast main line – one of the UK's main transport arteries.
"A high speed rail network, beginning with a line between London and the West Midlands, would provide a step change in the capacity, quality, reliability and frequency of rail services between our major cities," she said.
"A high-speed line offers potential economic and strategic benefits which a conventional line does not, including a dramatic improvement in connectivity between our major cities, Heathrow and other airports, and the rest of Europe."
The Countryside Alliance criticised the committee for failing to consider an upgrade of the west coast line as an alternative to building a new route through the Chiltern Hills, a protected area of outstanding natural beauty, while the TaxPayers' Alliance accused MPs of failing to subject the case for a "dismal white elephant" to serious examination.
"Taxpayers will be disappointed the transport select committee haven't done more to hold the government to account, and scrutinise this vanity project," said Matthew Sinclair, a director at the lobby group.
The Association of Train Operating Companies, which supports the line, urged the government to listen to concerns that investment in the existing rail network might lose out to the project. "The committee is right to point out that high speed should not come at the expense of investment in the existing network," said Michael Roberts, Atoc chief executive.
The Department for Transport welcomed the report as it prepares to publish the findings of a two-pronged consultation on high-speed rail, which is scrutinising the route for the first phase between London and Birmingham and asking whether Britain needs a high-speed rail network.
Despite opposition to the plans from Tory MPs and the London mayor, Boris Johnson, the government is expected to give the project the green light.
A DfT spokesman indicated that the response to the consultation has been largely positive. "The report provides a useful contribution to the debate on high speed rail, and echoes a number of the messages coming out from the responses to the public consultation."