The parents of the murdered schoolgirl Milly Dowler and the former landlord of Joanna Yeates have warned that plans to reform no win-no fee agreements will prevent people of "ordinary means" from obtaining justice or defending themselves in court.

They are among signatories of a letter released to the Guardian as the legal aid, sentencing and punishment of offenders bill – which the justice secretary, Kenneth Clarke, believes will do away with the "compensation culture" – returns to the Commons this week for its report stage.

The letter says: "We are all ordinary citizens who found ourselves in a position of needing to obtain justice by taking or defending civil claims against powerful corporations or wealthy individuals.

"We would not have been in a position to do this without recourse to a 'no win, no fee' agreement with a lawyer willing to represent us on that basis. As was made clear to each of us at the beginning of our cases, we were liable for tens if not hundreds of thousands of pounds if we lost.

"Without access to a conditional fee agreement (CFA), which protected us from this risk, we would not have been able even to embark on the legal journey."

Signatories to the letter, which has been co-ordinated by the media campaign Hacked Off, include Christopher Jefferies, the retired Bristol teacher defamed by the tabloids during the Yeates murder inquiry, and Bob and Sally Dowler, whose daughter's voicemail was hacked into by the News of the World. Others who have added their name are Peter Wilmshurst, a cardiologist sued for criticising research at a US medical conference; Robert Murat, who lived near the scene of Madeleine McCann's disappearance in Portugal and who sued British TV stations and newspapers for libel; and Mary-Ellen Field, Zoe Margolis, Nigel Short and Hardeep Singh.

All of them have had to resort to CFAs to seek justice.

The Ministry of Justice proposals will remove the ability of claimants to recover their costly insurance premiums and their own lawyers' success fees from losing defendants.

Instead, the costs will have to be paid out of any final award for damages. Opponents of the change, such as Hacked Off, warn that it will render the cost of seeking redress through the courts no longer financially viable and restrict access to justice.

Sally Dowler said: "At the outset we made clear that if we had to pay the lawyers, we could not afford to bring a claim; or if we had any risk of having to pay the other side's costs, we couldn't take the chance. If the proposed changes had been in place at that time we would not have made a claim. Simple as that, the News of the World would have won, because we could not afford to take them on."

The letter calls on MPs to support an amendment to the bill tabled by the Liberal Democrat MP Tom Brake, which would exclude privacy and defamation cases from the reform of CFAs.

Supporters point out that damages in privacy cases, for example, can be small and would rarely cover the cost of what might be a protracted legal case. Hacked Off is a campaign calling for a full public inquiry into phone hacking. Mary-Ellen Field used to work for the model Elle Macpherson; her phone was hacked. The writer Zoe Margolis sued a Sunday newspaper after it libelled her.

Dr Evan Harris, from the Hacked Off campaign which is working with the signatories to save CFAs in libel and privacy cases, said: "If these reforms go ahead in their current form the government will be making justice impossible for all but the rich. That may suit the tabloid interests and libel bullies but it's not fair."

A Ministry of Justice spokesperson said:

"There are many deserving cases brought before the courts. But we have

to stop the abuse of the system by others pursing excessive, costly

and unnecessary cases. Under the current arrangements, innocent

defendants can face enormous costs, which can discourage them from

fighting cases. This simply isn't fair.

By balancing the costs more fairly between the claimant and

defendant, these changes will ensure that claimants will still be able

to bring deserving claims, and receive damages where they are due.

Most importantly they will make the no-win, no-fee system sustainable

for the future."

• This article was amended on 1 November 2011. The original headline referred to legal aid cuts. This has been corrected.