He said it could be upgraded or downgraded over time depending on the perceived level of threat.

Such a 'middle-ground' arrangement would involve one or two protection officers travelling with Harry and were 'perfectly reasonable' to offer on a temporary basis.

His comments came as the row over whether taxpayers should fund the couple's security arrangements – which could cost £5million a year – deepened on Sunday night.

Labour's Dame Emily Thornberry said Harry, 41, Meghan, 45, and their children, Archie, seven, and Lilibet, five, 'deserved to be safe', while a Labour peer said they should pay for it themselves.

There was further confusion after a source close to the couple said their move to the UK could last for as little as six months.

A review is already thought to have been concluded by the Royal and VIP Executive Committee (Ravec), which oversees security arrangements for key VIPs in Britain, with Prince Harry reportedly 'privately pleading' with Home Secretary Shabana Mahmood for the result.

Lord Blunkett told The Times: 'There are three areas of security... the fully blown, blacked-out back-up car with two or three close protection – one in the passenger car and the others in the back-up – on a 24-hour basis. 

'There's then the middle ground... where you have one or two officers who travel with the principal, as they call it. The third is they get a driver with security training.

'The middle of that is a perfectly reasonable thing to offer for the time being, and then it could be reassessed in a couple of years.'

Dame Emily, chairman of the Commons foreign affairs committee, said: 'I would want to be reassured that his family are going to be safe. They deserve to be secure.

'He is the son of the King, he has made a big contribution to our country through public service – that puts him and his family at risk.' Fellow Labour MP Mike Tapp, a former Home Office minister, said a 'clear-eyed assessment of the threat' was needed for decisions about security.'

Tory leader Kemi Badenoch said: 'He's the son of the sovereign and that means he has a very high public profile, more than most politicians who get security.'

But Labour peer Lord Foulkes, a minister under Tony Blair, said the Sussexes' security was a 'private matter and they should deal with it personally'. He added: 'They are wealthy people and I wouldn't have thought it is something that the taxpayer should be expected to pay for.'

Other non-working royals, such as Peter Phillips, Zara Tindall and Princesses Beatrice and Eugenie do not receive police protection.

Andy Burnham has said the couple's security was a 'private matter'.

A Home Office spokesman said last night that it did not discuss private security arrangements.