The trust wants voters to show photo ID
Ministers are considering introducing individual registration for voters - as a report claims elections in the UK are vulnerable to large-scale fraud.
Justice Minister Bridget Prentice says tighter controls, including photo IDs, are being looked at. Currently only heads of households have to register.
It comes as the Joseph Rowntree Reform Trust suggests elections in the UK fall short of international standards.
The report comes ahead of Thursday's local elections in England and Wales.
It said measures to improve choice for voters - such as postal and electronic voting - are actually risking the integrity of the electoral process.
There have been at least 42 convictions for electoral fraud in the UK in the last seven years.
In 2004, a judge quashed the results of two local council elections in Birmingham after deciding there had been systematic large-scale postal vote rigging.
The problem is partly because "previously robust" administration systems have now reached "breaking point", says the report, called Purity of Elections in the UK: Causes for Concern.
It claims the benefits of postal and electronic voting have been exaggerated - particularly over claims of increased turnout and social inclusion.
The Trust wants all voters to show photo ID, and for campaign spending at constituency level to be capped.
It says the voting system is being undermined by political parties' spending on marginal seats.
There is "substantial evidence to suggest that money can have a powerful impact on the outcome of general elections, particularly where targeted at marginal constituencies over sustained periods of time," it said.
Report author Stuart Wilks-Heeg, a lecturer in social policy at the University of Liverpool, said: "It's very concerning that ministers tend to focus on 'quick fixes' to solve declining turnout and ignore genuine concerns about how easy it can be to cheat the system.
"The evidence continues to mount up and shows how we are desperately in need of an electoral system that robustly befits the 21st century, without belying our 19th century democratic roots."
The Electoral Commission said it had repeatedly called for the electoral process to be made more secure.
"We continue to urge the government to replace the current system of household registration with individual voter registration," it said.
"That would make the electoral register - the foundation of the electoral process - safer and more accurate."
The government says it has taken significant steps to protect the electoral process.
Ms Prentice, the minister in charge of electoral law, told the BBC: "We're looking at individual registration. We have increased the number of people registers to vote by almost a million."
Shadow justice secretary, Nick Herbert, says compulsory registration by every voter is the answer.
The Ministry of Justice says it is committed to ensuring people have confidence in the electoral system.
A spokesman said it had introduced measures to prevent abuse of the system, including new penalties and the tightening up of requirements for postal voting.
He said: "Election fraud is illegal, and police and electoral administrators work closely together to deal with any allegations."