It's illegal.
Under section 3 of the Road Traffic Act 1988, it is an offence to perform a clear act of incompetence, selfishness, impatience or aggressiveness which causes inconvenience to other road users.
In other words, driving without due care and attention.
The Crown Prosecution Service specifically include: "driving through a puddle causing pedestrians to be splashed" in its description of this section of the act.