It goes without saying a professional photographer should have public liability insurance and should be of the type specific for photography as it covers you should your photographer not be able to attend your wedding.
For further protection post wedding should things go wrong I would advise anyone to pay their wedding deposit with a credit card. This way you are covered under section 75 of the consumers credit act 1974 where should the photographer not deliver what you wanted for any reason or lost your images for example you are covered. Paying just the deposit actually will cover you for the whole amount of the agreement so even if you pay the balance with cash or cheque the entire amount is protected and the credit card company will fight your case to refund your money. Businesses need to have a direct merchant account with a provider, paying via PayPal of Google for example does not apply to the same regulations as credit cards.
So 2 things to ask for when considering a wedding photographer is ask to see a copy of the Public Liability insurance as your wedding venue may want to see a copy plus check what forms of payment your photographer will take. If they do not have a card payment terminal at your per-wedding consultation and can not show you an insurance certificate then my advise is buyer beware.