Car insurance cancellation charge

It will be in your terms and conditions and you will have accepted the terms and condiions when you took it out. So no way out I'm afraid.

Can i claim that this is an unreasonable charge... it certainly seems like one

Hello purplicity - Welcome to the site.

There are many reasons why this is not unreasonable that you might not be aware of, so I will do my best to explain.

1) You probably agreed to this and it is probably in the documents sent to you. I appreciate the difficulties in reading large amounts of paperwork, but it's still your responsibility to make sure you are happy with the contract. If you are not happy, then there is a "cooling off" period to deal with that.
I find it better to check things out up front as it's less hassle not to start a policy rather than try to get refunds. Companies have a habit of losing cancellation letters and being slow with refunds, so it's just less hassle all round to bit pro-active.
2) It is quite legal.
3) Insurers spend a certain amount of money providing free quotes and setting up policies. If you cancel early they are entitled to get back some of those cost. The cost involved are setting up call centers, providing staff to answer phones and computer hardware and software for the quotation system.
3) Insurers have some legal/regulatory obligations. For example they have to keep your data secure and they have to keep it available for 6 years before disposing of it. That all costs money.
4) There are actually some costs to them in closing your policy. This includes computer hardware & software which all has to have security and back ups in place.
We all expect them to keep our data safe and not to lose it and there is a cost attached to this. I work in IT and the costs to implementing security with banking details is not insignificant.

I hope this helps explain some of the costs involved that might not be immediately apparent to you.

If you want to check costs out in future then I would suggest the following site (no connection).
https://www.matthewsguide.co.uk
which has some info on the charges for different insurance companies.
This may save time trawling round the net and checking out each company individually.

I hope my explanation may allow you to feel a tiny little bit better about paying it, if you appreciate the kinds of things that it's for rather than just another "rip-off" charge.
I don't believe that insurers generally are making massive fat cat profit margins although of course as with every other business their prime function is to make money.