For a long time HMRC didn't make VAT vs Income tax connections, and it was pretty easy to suppress revenue, but about 7 or 8 years ago one of my clients had a joint review where they did match VAT to self assessment (we passed OK) and I remember thinking it was the right approach. Now with digital tax returns being required for VAT and soon self assessment that will be much easier to do. Of course what it will mean is that more "miscreants" will simply not register/deregister for VAT or report income for self assessment, and at the same time increase customer prices to cover the VAT they can no longer recover legitimately.
However, as our dear departed socialist worker representative would say, tax revenue lost in the grey market morass is nowhere near as much as that lost by multinationals transfer pricing profits to low tax environments. I'm not sure which is the greater source of hemmorrhage to HMRC but I suspect the grey market is the easier one to fix

