MPs have passed a bill that would allow British law enforcement agencies to seize the UK assets of dictators and rights abusers, even for offences committed overseas.

The Commons unanimously passed the third reading of the criminal finances bill, a wider measure that adapts the earlier Proceeds of Crime Act, allowing police to target “unexplained wealth”.

The bill was passed with an amendment that means assets can be seized from people who have carried out “a gross human rights abuse or violation” outside the UK.

The government-sponsored amendment was included following heavy cross-party pressure from MPs for action to tackle the flood of money entering the UK from corrupt politicians, criminals and others.

The National Crime Agency says it believes up to £100bn of tainted cash could be passing through the UK each year, with significant sums invested in property, particularly in London’s booming high-end market.

A collection of 50 MPs from various parties, led by the Conservative Dominic Raab, came together to propose an amendment that would have allowed NGOs and individuals to seek to persuade a senior high court judge to seize the assets of a rights abuser.

It called for a public register of those whose assets had been seized and would have placed an obligation on ministers to seek an order if they were presented with compelling evidence of abuse and it was in the public interest to do so. The amendment was named after the Sergei Magnitsky, a Russian lawyer who died in prison in Moscow in 2009 after exposing an alleged $230m (£184m) fraud carried out by leading Kremlin officials.

But Raab agreed to drop the measure in favour of the government’s amendment, which does not allow NGOs or individuals to seek orders.

Speaking in the Commons, Raab said it was estimated that £30m of the money exposed by Magnitsky had been sent to the UK, with no action from the police. It was “by no means an isolated case”, Raab said, arguing that Britain must do more to tackle money connected to rights abuses.

The UK must remain open to investment, he said, adding: “But I also want us to be known the world over for our integrity, too. I want us to be known the world over for our commitment to the rule of law. I want us to be known for our adherence to the most basic of moral principles.

“And that means we have to stop turning a blind eye to the blood money of butchers and despots which, frankly, flows all too freely through some UK banks, businesses and property.”

Raab said the government’s amendment was not as robust as the one he led as it placed no duty on UK law enforcement agencies to act and had no provision for third-party applications and no public register. But he agreed to drop it after the security minister Ben Wallace said the government would act rigorously in pursuing the assets of rights abusers and would publish annual data on how often the measure had been used.

Among the MPs who backed Raab’s amendment were the Green party co-leader Caroline Lucas, the Ukip MP Douglas Carswell, the Labour MP and former public accounts committee chair Margaret Hodge, and members of the Scottish National party and Democratic Unionist party.

The wider bill is intended to significantly improve the government’s ability to tackle money laundering and corruption, recover the proceeds of crime and impact terrorist financing.

It follows an anti-corruption summit hosted by David Cameron in May and revelations in the Panama Papers that foreign autocrats and their families used offshore structures to buy London property.

The bill will go to the Lords before becoming law later this year.

Wallace said the amended bill would see the UK become “a hostile environment for those seeking to move, hide and use the proceeds of crime”. He added: “The UK simply cannot be seen as a haven for dirty money.”

The government had agreed to the rights-based amendment on asset freezes after seeing the “strength of feeling” from MPs, he said.