The Metropolitan police could axe up to 5,200 officers by 2020 in a bid to meet a black hole in funding, according to Labour.

The party, which analysed figures from the House of Commons library, found that the force could lose between 1,300 and 5,200 officers – out of a total of 31,000 – by the end of the decade under George Osborne's cut state spending.

"Osborne's plans for cuts in Metropolitan police funding ... would have a devastating impact on the quality of policing in London and be the final death knell for high visibility, bobby on the beat local policing," said Gareth Thomas, the shadow London minister.

Bernard Hogan-Howe announced that the force plans to save £400m ($623m, €509m) by 2020.

Labour asked the Commons library to investigate the impact on police numbers if the force sought to achieve the cuts by reducing the force's headcount.

The library calculated that the average cost of a police officer in London is £77,000.

The study found that if the Met has cut its budget by £100m in 2016-7, it would have to cut police numbers by 1,298 on officer reductions alone.

If the same level of saving is required for each of the four years, the research revealed that up to 5,194 jobs would be under threat.

"Police spending cuts do not mean simple salami slicing of police officer numbers," a Home Office source told the Guardian.

"And police officer numbers are not the test of how to cut crime – what matters is how they're deployed, not how many are employed.

"The experience in this parliament – in which we've cut spending by 20% and crime has fallen by more than a fifth – shows that it's possible to do more with less."

Mike Penning, the policing minister, added: "There is no question police will still have the resources to do their important work.

"Her Majesty's Inspectorate of Constabulary recently found that forces can successfully manage to balance their books while protecting the frontline and delivering reductions in crime.

"We have made it easier for the police to do their job by cutting red tape, scrapping unnecessary targets, and giving them the discretion to use their professional judgement."