The government has also been told to do more to challenge the Chinese state on what MPs say is "unfair trade practices."
Chinese firms are subsidised by the government and so can sell their steel at loss-making prices, undermining British firms which are not bailed out by the state.
While the US authorities can investigate claims of dumping and take action in just two months, the European authorities take as long as 18 months to come to a decision. As a result, ministers should push the EU to work faster, and should act directly to take a harder line with China, MPs said.
"We acknowledge that the government has raised the issue of the overproduction of Chinese steel on a bilateral basis and at an EU level," said the report. "But no tangible action or agreement has come out of it. We are therefore concerned that this is merely talking with no improvement for the UK or European steel industry; much more sustained pressure is required."
The government said there was little more it could have done.
"We have taken clear action on relief for energy costs, anti-dumping, procurement and EU emissions directives, meeting key industry asks. Whilst the government is doing all it can to help the industry, the government cannot dictate the commercial decisions, operations or financial performance of private companies," said the Department for Business, Innovation and Skills.
"SSI UK had lost over £600m in just three years, had accumulated even greater debts and the price of the steel it produced had halved in the past year alone. If the BIS Select Committee had a magic bullet that could have saved the plant against these conditions, they certainly kept it to themselves."
The report also blamed Britain's steel industry itself for some of its own woes, as steel manufacturers failed to spot the trends in global markets.
"It must be the responsibility of the industry itself to predict and respond to long term trends in global production and consequently prices," the MPs said.
The Committee said that little can now be done to save the skills of the workers in Redcar, meaning a substantial chunk of an industry which the government says is of strategic importance to the UK economy and to areas such as defence is now gone for good.
"My concern is that the government should have explored much more thoroughly options to keep the Redcar plant open to retain the industrial assets and the skills rather than washing its hands too quickly, allowing it to close down and inflict severe damage on future manufacturing capability," said Iain Wright, the Labour MP for Hartlepool who chairs the Committee.
"Failure to consider effective mothballing not only undermines capability for the UK steel industry in the future but could cost the taxpayer a fortune in clean-up costs. This approach is concerning should other vital plants the UK steel industry also face closure as a result of the global pressures on the industry."
Industry group UK Steel welcomed the report.
"Immediate priorities are the tackling of Chinese dumping of cheap steel at EU level and a firm commitment from government to ensure that all major procurement projects, from rail to tidal barrages and airports, use British steel to give this vital UK industry confidence for the long term," said director Gareth Stace.
"Business rates must also be reformed to avoid some of the penalties steel companies and other manufacturers face if they invest in plant and machinery."
The SSI plant in Redcar closed in October with the loss of 2,000 jobs and a financial hit of £530m for its owners.