This is an employers liability claim - I used to work in this sector. You need to write a letter to the legal/insurance department of your company saying that you wish to make a claim for compensation, and asking them to pass it to their insurance company. However, it is much better to appoint your own solicitor and ask them to do this for you and to act for you - since the insurance company will almost certainly do the same, and if you are trying yourself to work your way through the system about negligence and employers' liability, you need to be very much on the ball about H&S leglslation, reasonable doubt, etc. The best thing you can do is go to your usual solicitor and ask them to act for you. Yes there are no-claim-no-fee solicitors but as BM says many are centralised and won't know your area. If you have to pay then you do, but fees are not payable until the claim is finalised, and if you win, then the employers' insurance company should be paying all your costs, not you.
Don't discuss what you are doing with your employer - once the claim has gone in, they are not allowed to discuss it with you while the claim is being investigated.