If I had the numbers and letters of someone's car plaque, could the police identify them?
The police can identify the legal keeper of the car which legally carries that license plate. I assume you are interested in the identity of the driver; if you have the identity of the legal owner then the legal owner very often can identify the driver - especially important if the car is a rental car; the rental car will known who was in posession of the car at any time.
There will be cases where you are stuck or where it's difficult: If the car was stolen, if the car was sold to an unknown stranger without informing DVLA, or if someone created fake license plates. The police in the UK also seems to have problems finding drivers of cars with foreign license plates.
Well, it depends.
In the UK, car registrations are required by law to be kept up to date with the DVLA with regard to keeper of the car (ownership is a different concept) and their address, so if the person to be identified is the keeper and they have complied with the law, then yes.
Note that there are a number of companies which also have access to the DVLA vehicle and driver licensing databases, so not just the police can perform a lookup.