Notice served on a no-notice contract as contractor eyes small claims

I was given 4 weeks notice on a no notice contract, the agent says it wouldn't be good for us to go to court

I started a 3 month contract via a well known agent. Four weeks into the contract it became apparent that the headcount was never signed off and I was given written four weeks notice and have a nice Christmas.

The contract itself stated that the notice period is as per the attached schedule. The schedule states notice period as 'not available'.

There are some contingencies for bankruptcy, war, acts of terrorism, etc. I have also noticed that there is a section stating that the contract may be terminated by written mutual consent.

Clearly none of these are applicable and with Christmas looming I want some compensation.

I did mention this to the agent of said large agency who fluffed and talked about not falling out and courts, etc.

The value of fees that I will lose are in the region of £4500 + VAT and I am thinking of the small claims court to recover this amount.

Is there someone who can I pay to look at this contract and state whether I am reading the contract correctly?

I would also be interested in what steps to take prior to issuing said small claim, should I send them a final demand and should I request interest if payment is not forthcoming within a specified date?

I have luckily found another contract whilst in my 'notice' period, I don't think this should make a difference as there is still clearly in my opinion a breach of contract?

Any help/ideas/suggestions would be greatly appreciated.

thanks

Neil