cut off fingers left hand at work

I hope you told your employer that you are injured at work. This is the first and most obvious thing to do, if no one knows that you were injured then it is going to be very difficult to make a claim for compensation later on.
Your employer should carry out an investigation into the accident whether you are claiming compensation or not. With most accidents the employer should make a written report of the accident to the Health and Safety Executive (HSE). The HSE is a government body responsible for investigation of accidents. They have powers to investigate accidents. They can prosecute companies for the most serious cases. They do not have the resources to investigate all accidents but because the employer has to report the accident to the HSE in most cases it is possible to see what the company said about the accident in that document. In cases where there was an investigation the HSE report can be obtained.
If you wish to make a claim for compensation you can do so if your employer was to blame for the accident. The employer must have insurance to cover liability for the accident. Earlier you have to prove a case of negligence or breach of statutory duty to win your case.