I dunno why they don't make it so that businesses have to claim tax credits to top up wages, instead of workers. So set an arbitrary minimum wage of whatever (say £10 an hour, which is probably around the level of the actual minimum when in-work benefits are added), then give small businesses a subsidy to pay for it (topping up a £6 an hour wage to a £10 an hour legal minimum, for example). Larger corporations making vast sums can be hammered politically so as not to take the government wage top-ups, or take less of them. The cafe owner gets help to stay in business and pay the waitress, and the workers don't have the hassle of having to claim tax credits to top up their wages, they just get paid a proper living wage. And if big business keeps dodging tax in a way that small businesses cannot, then the government can withdraw wage subsidy for such businesses and still enforce the much higher, legal minimum wage. So in that way, we might also level the playing field between smaller businesses and big corporations. It would also end the discrimination where a worker who is single and childless gets paid less than a worker who has a family, yet they do the same job.
I'm sure there's a ton of reasons why it can't be done, but in a nutshell: tax credits to businesses instead or workers, higher minimum wage to workers.