Senior Tories have raised concerns that the party is risking its reputation for being strong on law and order as the police unveiled plans for a summer campaign of protest against coalition cuts.

Officers from more than 40 forces will put their case against the government's cost-cutting and wider changes, at a meeting in parliamenton Monday, while the Police Federation, which represents the rank and file, has announced a national "day of action" in July aimed at derailing the current policies.

David Davis, the Conservatives' former home affairs spokesman, expressed fears that the party was in danger of losing its reputation for being tough on crime and that public confidence was being dented by cuts to the police and justice systems combined with new liberal sentencing policies.

After a week in which the justice secretary, Kenneth Clarke, caused a storm over proposals to offer shorter sentences to rapists who confessed at an early stage, Davis said: "There is a serious risk that the Conservative party will lose its clear 20 to 30 point opinion poll leads [over Labour] on crime and immigration if it does not take a clearer stance on these issues."

At the same time, Labour moved swiftly to fill what it believes is a policy void. The party's home affairs spokeswoman, Yvette Cooper, pledged to set up an independent commission on the future of the police – while it is still in opposition – if ministers continue to refuse to do so. The independent commission would draw on evidence from police officers past and present as well as law officers and academics.

The Police Federation, which represents 138,000 officers, said it had never experienced such dire relations with any government. Its president, Paul McKeever, said: "It's the most difficult time anybody has ever faced in the lifetime of the federation." In a sign that police were happy to work with Labour, McKeever offered his full support to Cooper's proposals.

"We will be speaking to her about it. [Labour's] heart is clearly in the right place in relation to understanding the need for a review. It's encouraging to see that there are people within parliament who are actually listening."

He also revealed the first details of a rolling programme of protests, including a "major event" in July. The events would culminate in officers targeting the Conservative and Liberal Democrat party conferences this autumn if the plans have not been dropped or drastically changed. The federation says that spending cuts totalling 20% over four years will lead to the loss of 20,000 jobs. These concerns, and those on pay and working conditions, will be aired in parliament during a meeting hosted by the Labour MP Keith Vaz, chair of the home affairs select committee.

The emergency meeting, to debate the future of policing, will begin with an introduction by McKeever and hear concerns over the Winsor review, which is examining police pay and conditions, and ways to tackle bureaucracy as part of the committee's inquiry into policing.

The Observer has also learned that David Cameron and George Osborne, the chancellor, are deeply worried that the need to cut back on the police, prisons and wider criminal justice budgets is making it near-impossible to maintain the Tory reputation for law and order.

A senior source said that officials from No 10 had recently held talks with justice ministers to discuss how to make their policies look tougher. Police anger is focused on the impact of the proposed cuts and changes in pay, pensions and working conditions. The government's desire to install elected police commissioners in place of chief constables has also raised concerns. The Home Office argues that the planned changes are necessary and will help cut red tape.

Cooper said that the coalition was creating "a perfect storm around crime and policing – and it is communities that will pay the price".

She added: "They are making massive cuts to the police and to their powers, hitting youth services and prevention programmes, cutting sentences for serious offenders who plead guilty and bringing in American-style commissioners which puts significant policing power in the hands of one politician with no proper checks and balances.

"David Cameron is badly out of touch with the public on crime. Chaos and cuts are a toxic combination when it comes to keeping communities safe."

There is a growing sense, meanwhile, that austerity measures are being used by the government to reshape policing, which is seen as the last unreformed public service. Privately, Cameron is being singled out by senior police figures who point to his role as a special adviser in the last Conservative government which was humiliated in its attempt to change police pay and conditions. The accusation surfaced that the government's plans to impose 20% cuts on the service was a form of retribution by Tory ministers.

The last large-scale review of policing in Britain was the 1962 royal commission. Since then, senior officers argue, the remit of the police has expanded into dealing with international terrorism, cyber and organised crime, and local concerns such as antisocial behaviour.