They should have sent you a written quote a few weeks ago which should have mentioned the automatic renewal, unless you made contact before a certain date. If you have the opening hours in writing which were not honoured, you should be able to cancel as soon as they opened today. A cancellation fee does not seem right. You should tell them that you do not accept this and, if they still take a direct debit, you should tell your bank about the situation including mentioning that the charge was not authorised and ask them to start their disputes process. If you are willing to stand up to Budget and reject what they are trying to do, you will need to start the other policy to have cover.

Inform them unless they waive the unreasonable and unfair charge caused by circumstances of their own making, that you will make an official complaint about their sharp practice to the insurance ombudsman at the FOS.

http://www.financial-ombudsman.org.uk/consumer/complaints.htm

My car insurance was due to be automatically renewed on 2/1/09. I found a cheaper quote online and decided to cancel my policy. I knew Budget would be closed New Years day so I phoned to cancel when I got home from work on New years eve at 5.30 only to find they had closed. The recorded message said they had normal working hours but were closed New years day.The letter I had and the website said they closed at 9pm. Budget do not have a contact e-mail address but ask you to phone them. Now they say I have to pay a cancellation fee. They argue that I had the 27th,28th and 29th to cancel but surely I have the right to cancel up to the last minute of their working day and if they change their working hours without making it public then how would anyone know to phone earlier!