Putting your parents as first driver and you as named driver is illegal and they are really cracking down on it. It's called 'fronting' and the companies are really wising up and will refuse to pay out and take you to court if they even have a hint of it.
Shopping around is the way though, also take into account your mileage since companies (some especially) offer decent discounts for people doing under 7000 or so miles a year.
I always find www.moneysupermarket.com gives me better quotes than the other comparison sites.

