One or two here have hit on the main problem with a national force. Whilst there will no doubt be nods towards local policing, all policies and procedures would be decided upon centrally.
We already have examples of this, stretching back years. After the riots in the '80's it was decreed by the Home Office that every police division should have a liaison officer for ethnic minorities. At the time, not a bad idea in parts of the big cities. Build bridges, get to know them, keep tabs on them. But that also meant that places in, for example rural Cumbria also had to have them. So you end up with an officer in an office not looking out of their window in the morning, because then he'd have nothing to do in the afternoon. On his way home he could pick up a Chinese one time and an Indian the next. Job done, not only had he liaised, he had actually visited everyone in his area that was a member of a minority!
There would be advantages in procurement savings and savings on salaries for senior officers, which is good. But really the only savings would be financial. I don't know about anyone else, but it seems to me that the government want us to have a police service like they do in European countries. Where there's no regular contact with the public. Even now, try calling your local force to speak to an officer. Easier for a camel to pass through the eye of a needle these days. Or call at your local police station. In all likelihood it's been closed and you'll have to go to the nearest big town. Where you will still be lucky to speak with a real police officer. Where reporting many crimes is pointless as nothing can be done. Where even major enquiries are compromised to the point of incompetency (think Madeleine McCann).
One thing we did have here are police forces to be proud of when you compare them to the rest of the world. We are already far along the route of seeing them becoming at best, ordinary. This would be just another step in that direction. But it would save a bit.