Not the UK but in the 1970s my then GF and I witnessed a serious accident. One driver (not the one at fault) was seriously injured. The police sat each of us in a patrol car (separate cars, different officers) and took our statements right then and there.
Later, the wife of the badly injured driver called me to thank me for my statement. The guy who caused the accident (speeding -- a LOT! -- and running a red light long after it had turned red -- no "but it was yellow when I entered the intersection") told the police that he had been heading in the opposite direction from the direction he was actually driving, and he told them that the injured driver had cut him off. And that's also what he told his insurance company, so the insurance company initially was going after the guy who was seriously injured. Until an insurance investigator called me and I set him straight as to what actually had happened.
But that was the USA. I don't know how the police operate in the UK.