What are the figures behind this? The number of police officers in England and Wales has already fallen by about 16,000 since 2010 because of cuts in Home Office funding. Labour's sums are based on assumptions about the amounts all unprotected government departments are likely to have to be cut to meet the targets for cutting the deficit, which were set out in the Budget. The Conservatives are yet to set out plans for the next three years of funding for the Home Office.
Labour says it has identified Â£800m of savings that could be made in police forces, which would prevent the loss of 10,000 jobs that it says the Conservatives would have to cut in the next three years. Labour's figures assume that all departments will be cut by the same amount. Of course, when the next government has its spending review, it could decide to make much more severe cuts to some departments than others.
Labour says it will save Â£800m by doing things such as scrapping the elections for police and crime commissioners, which are due to take place next year, and making people pay the full cost when they apply for a gun licence.
The Conservatives respond that scrapping commissioners and other measures would not save as much as Labour claims and that they have already announced plans to increase the fees for gun licences.
The biggest proposed savings come from making it compulsory for police forces to buy things together to increase their negotiating power.
The Conservatives say that already happens in a lot of cases but that Labour has overestimated the potential savings.
The Tories also point out that, despite the falls in police numbers over the past five years, crime has fallen. The two things may be unrelated and crime has been falling since the late 1990s.
So it is difficult to demonstrate either that if the Conservatives were to win the election they would cut 10,000 police staff over the next three years or indeed that Labour's plans would prevent that happening.
What this argument does highlight is how tight a timetable the next government will be working to. Departments only have spending plans laid out for a year from now.
The previous government did not manage to have a spending review until 20 October 2010. There is frantic contingency planning going on all over the civil service. And we know the police are preparing for further cuts.
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Labour says it is going to protect 10,000 police jobs, which would otherwise have been lost over the next three years.