Surely Police in the UK have the right to stop and require people to identify themselves, especially when in a car.
No. If you are driving a car, the police can stop you for any reason and you must present your documents (driver's licence, registration, MoT and insurance). But you don't have to carry them on you and if you don't you need to present them at a police station within seven days. This only applies to the driver.
At other times, the police have the power to stop and question you at any time. They can also search you, if they have reasonable grounds to believe you are carrying drugs, a weapon, stolen goods or something used to commit crimes (I guess any tools would count there). But you are not obliged to show them any identification.
In fact many people don't carry photo id around. There are no id cards and older style British driving licences don't even have a photograph on them. I got a new driving licence with my photograph on it last year and that was only because a photo licence will be mandatory from 2015.