The obligation under s. 172 RTA 1988 to name the driver is personal, but the performance need not be (unless the addressee was the driver). When the police state that the form must not be passed to the driver, they are variously pointing out that if the driver then decides to ignore the form it is the addressee that commits the s. 172 offence, and engaging in their favourite hobby of making up imaginary rules/laws.
There is no reason why the OP cannot respond on behalf of the RK, with the RK's permission, naming himself as the driver.
The only issue is that the OP must understand that doing so does not negate his own obligation to name the driver when he subsequently receives a notice in his won name.