It absolutely needs government interference. Ever think you’d hear a Tory say that?!?!!!
Right now the government is interfering by paying working tax credits - that is a clear admission that people are not paid enough. So we have tax payers subsidising corporate profits.
The only solution is to force inflation. There are two levers the government can pull IMHO here, public sector wage rises should prompt some equivalence in the private sector and secondly, more brutally, through taxation - tax profits at 100% for anyone not paying a fair wage (TBD) - obviously some exceptions would apply. I suspect that many of the companies who don’t pay are high street type names who wouldn’t flee the UK and ultimately they would just put their prices up (inflation). It wouldn’t be an overnight thing but rather would need to be introduced over the course of x years to stop it being a shock event and would need some bright sparks to work out the details. It would also be a true Brexit benefit as the workforce is domestic and finite without freedom of movement.