Hundreds of billions of pounds could be being laundered through the UK every year, but the government is unable to give a precise figure of the scale of the problem, MPs have found.

In a report on economic crime, the Treasury committee said the scale of the problem in the UK was very uncertain, with estimates ranging from tens of billions of pounds upwards.

It called on the government to provide a more precise estimate in order to formulate more effective strategies to tackle the problem.

It said the UK government should regularly review its efforts to crack down on money laundering, and should not compromise on supervision when securing post-Brexit trade deals.

The report comes after the Guardian and partners around the world revealed how Russian money had been channelled into the UK and used to pay for everything from luxury properties and cars to school fees.

Speaking earlier this week, the minister for national security, Ben Wallace, said it was wrong to think of money laundering as a victimless crime. “Those with dirty cash to clean don’t just sit on it,” he said. “They reinvest it in serious organised crime, from drug importation to child sexual exploitation, human trafficking and even terrorism.”

The committee said the government’s efforts to improve action against companies involved in economic crime seemed to have been stalled by Brexit, and warned the UK’s departure from the EU presented “both risks and opportunities”.

Its chair, Nicky Morgan, said the government “must ensure it does not bow to buccaneering deregulatory pressures and maintain its intentions to lead in the fight against economic crime”.

The committee said the UK’s system to prevent money laundering was “highly fragmented”, with 25 separate organisations supervising the checks, many of them trade bodies for accountants and solicitors.

It said this was of particular concern where property and company formations were concerned.

Estate agents have previously been criticised for not doing enough to prevent the proceeds of corruption being used to buy UK property, and the committee said HMRC should ensure that they were all registered and following best practice.

Earlier this week, it was announced HMRC had carried out spot checks on 50 estate agents and, separately, that it had fined the property firm Countrywide £215,000 for failing to comply with regulations.

The committee’s other area of concern, company formation, was highlighted when the Guardian revealed that hundreds of UK firms had been used to disguise the sources and beneficiaries of millions of pounds’ worth of transactions.

The agency that registers UK firms, Companies House, is not required to carry out anti-money laundering checks, and the committee said this weakened the UK’s system for preventing economic crime.

It said the government should urgently consider giving it powers to verify information given by those forming new companies.

Morgan said: “With the uncertainties of Brexit around the corner, the government should regularly review the UK’s effort to combat money laundering to ensure a constant stimulus to improve.”

She added: “The government needs to bring greater order to a fragmented supervisory system, better identify the scale of the problem, and make a greater effort to combat the known risks and gaps in the supervisory system.”

Duncan Hames, the director of Policy Transparency International UK and one of the witnesses who gave evidence to the MPs, said he welcomed the serious attention being given to the “flood of dirty money into the UK”.

He added: “The committee’s report reinforces our own findings that the UK economy is vulnerable to abuse by corrupt individuals who have made it a key location in which to launder the proceeds of their crimes.

“Police estimates for this problem have repeatedly been of the order of £100bn a year, it could be far in excess of that, but what matters now is not how much more, but how we respond.”

A government spokesperson said: “There is absolutely no place for illicit finance in the UK, which is why we’ve made targeting economic criminals a priority. We’ve passed legislation on criminal finances and bribery, developed powerful new tools for law enforcement, and created the new National Economic Crime Centre.”