I don't know of a website that can advise you, but it will depend how much you want to invest in changing over.
If you're on economy 7, you could think about switching to economy 10. This gives you three extra hours of heat which might make all the difference. Otherwise, you need to look into swapping the storage heaters for convectors, but expect to pay more in bills.
Otherwise research the capital costs and running costs of oil central heating.