As with anything requiring logic or common sense, it wouldn't have any effect. This crowd giving guff about scroungers tend to be the same people who think tax is theft. They don't want to crack down on wealthy tax-dodgers. They aspire to join them.

I’m not convinced there’s really a significant libertarian constituency in the UK like that. I think the sentiment is more: “I work hard and pay my taxes, as an honest person should, and others are taking the piss.”