Allan is right - it'd be essentialy the system they have in Ireland. But I'd worry that the voters in England would be less wise in their choice than their neighbours in Ireland. I can easily see them going for a celebrity, or a retired politician. Unfortunately David Attenborough is too old to do the job.

Actually I suspect they'd very likely go for Prince William

The nightmare of course would be if England went down the executive president model of America, Russia and France.