Pragmatically, the minister is probably taking the right approach...
Any company outright claiming or more subtly creating the impression they're someone else is presumably breaking one law or another, be it trademark-infringement, rules about "passing off", or downright fraud "obtaining goods or services (or payment) by deception".
Problem is, while the government and parliament takes much pride and song-and-dance about creating new laws, we seem to be increasingly impotent at enforcement. The authorities, police, whoever, increasingly don't seem to have the balls (or resources?) to deal definitively with dodgy businesses - or pussyfoot around giving them "words of advice" and time (years) to "give them a chance to improve their practices" - a frankly quaint approach, totally out of touch with the realities, pace, and attitudes of today's world.
This goes doubly so for scams which are primarily online or promulgated by telephone.
"We're phoning you on behalf of Lloyds TSB, Barclays, and BoS about your PPI refund." No you're not. You've got no official connection with any big-name bank. These calls/texts have been going on for 2 years, yet nothing seemingly is done. They fall between the cracks of OFCOM, Phone Pay Plus (or whatever they call themselves this week) and I-don't-know. And nobody bangs their heads together and tells them to stop passing the buck and sort it. And the gov is totally unimaginative in envisaging the gaps between all these regulatory bodies when it sets their remit (or is bamboozled by too many lobbyists with vested interests).
Deceptive websites fall into much the same category. Except that as far as I'm aware there's no specific body to chase them, and the basic plod probably wouldn't know where to start.
Add to which both the websites and telephone scams may well be run from outside UK jurisdiction.
So actually, chasing Google (a single point of call, who isn't going to merely disappear today, then pop up tomorrow under a new trading name after months of "investigation" and "words of advice") and asking them not to screen misleading ads is probably actually the least-effort way for ministers to get the result they seek. Even if they don't have legal powers to enforce G to do anything,
As a longer-term strategy however, the gov has got to get to grips with enforcing the law properly through suitable channels which are up to the task.