The Government has its hands on a lever that would make short-term speculation markedly less attractive than long-term investment.
An increase in the cost of stamp duty, the UK's levy on the purchase of shares, would directly discourage trading. Short-termism has grown as trading costs have fallen, cut by the increased efficiency of electronic trading systems and competition; pushing up stamp duty would be a direct way of countering the trend.
This would be blunt, of course, but the Government need not be so siplistic. A significantly better change would be to modify stamp duty, so that it was charged on sellers of shares rather than buyers, and tapered to zero if the shares had been held for a certain length of time - say, three years.
I should point out that I'm not personally convinced this is a good idea, for reasons I set out here. I'm inclined to the view that it would be better if pension funds and others made a concerted push to reduce unnecessary costs, including high turnover, rather than seeking to whack the problem with a tax. But it's interesting to note that such ideas are getting a decent hearing these days.