Reform has been critical of measures contained in the bill and the impact they could have on funding the party receives from donors.
There are currently no restrictions on the amount of money UK-based donors can give to political parties and politicians.
Labour MP Stella Creasy said donations from individuals and companies giving £1m or more had “surged” in the last decade and gave examples for different political parties.
Among those she named was British billionaire Christopher Harborne, a Thailand-based businessman, who is one of Reform’s biggest backers.
Last year he gave a single donation of £9m to Reform – the biggest single donation to a UK political party by a living person.
Creasy was among those who tabled amendments seeking to also impose a cap on UK-based donors.
One of her proposals called for an immediate £500,000 limit which would reduce to £100,000 in the second calendar year. Minsters would have been able to set a permanent cap.
The amendment, which was not moved to a vote, was signed by more than 60 MPs.
Creasy told the Commons: “Obscene wealth is increasingly dictating who is heard, whether we like it or not, what issues are being prioritised and whose interests shape policy decisions.”
The Walthamstow MP added that there was a “need to act now to protect the next general election”. Her proposals would have exempted trade unions from the donation cap, with the MP saying this is “already well regulated” and “clean money”.
Kruger highlighted the millions of pounds donated by trade unions to the Labour Party as he criticised the proposals and the bill.
The MP for East Wiltshire said: “The claim is made that this bill will defend democracy, but actually it’s a flagrantly partisan attempt to kneecap Reform UK.”
The former Conservative MP added: “The suggestion is made that this bill will restore trust in politics and that is exactly what is needed.
“But what they all mean is to restore trust in the class of politicians and in the political parties that have got us into the mess that we are in, including the party I’m afraid to say I was part of which is why I left it. We need change.”
Responding for the government, Eshalomi said the bill “already contains a package of significant measures designed to strengthen the political finance regime whilst ensuring that legitimate donors can continue to fund election campaigns”.
The communities minister added that the prime minister was among those “determined to tackle the UK-based issue of mega-donors in UK politics”.
“That is why I’m happy to commit and announce the new cross-government task and finish team will be working at pace to find a solution without unintended consequences,” Eshalomi said.
“I can reassure members that once these solutions have been found, we would want them in force as soon as possible.”
Full details of the new team’s remit have yet to be confirmed by the government.
It last month emerged that Burnham registered accepting £345,000 of donations over the past year, including £164,347 from businessman Lord Sainsbury.
The Liberal Democrats proposed establishing a royal commission to make recommendations for a cap on political donations and the “effectiveness” of existing campaign expenditure limits.
This proposal was rejected in the Commons by 427 votes to 85, majority 342.
Green Party MP Ellie Chowns said Creasy had made a “clear case” for a cap on all donations, adding she would prefer it to be lower and suggested £50,000 a year.
Conservative shadow housing secretary Katie Lam said it was a “noble aim” to protect UK democracy from foreign influence but changes proposed by the government had not always been produced with “proper care and attention”.
In March, the government said donations in cryptocurrency to UK political parties would be banned alongside the move to cap donations of British citizens living abroad at £100,000 annually.
Ministers later announced overseas voters moving to the UK would be prevented from giving more than £100,000 in political donations for a year after their arrival.
This was announced alongside tougher checks on company donations, which they believe will help stop foreign money from influencing UK elections.
The bill also contains measures to change the voting system, including extending the right to vote to 16- and 17-year-olds.
MPs approved the bill at third reading by 411 votes to 102, majority 309, and it will undergo further scrutiny in the House of Lords at a later date.