Can some one please point me in the direction of a case where it was better to settle out of court rather than go through the system and pay solicitors and barristers, if the company shows that contributory negligence was involved would it be better to agree a payout out of court?

I very much doubt the answer will be found here. Invariably the answer will depend on any number of factors and the specific and pertinent details of the case. As this a H&S forum I assume the claim is for personal injury or ill health? I which case I suggest you pass this to your insurer without delay, if you already haven't, and let them deal with it. I hate to say it, but it isn't for this forum to try and decide, especially on the basis of the details that have provided.

If the claim is settled out of Court then there won't be a 'case'. Only a Court can confirm if contributory negligence was a factor. Claimant/defendant can onlt make claim/speculate in that regard. Out-of-Court settlements are a matter of routine for larger bodies such as Local Authorities ( with their Insurers) settling small claims in the £2-4K range.

Years ago I was told by my employer that it cost about £20K to walk through the court room doors so many companies and insurers were happy to pay out small amounts rather than fight a case. I dread to think what the cost would be now to walk through the doors as this was about 14 years ago. I have seen many spurious requests for information such as toilet seat checks after an employee fell off a toilet seat and was seeking compensation and such requests will often lead to a payout as there was no way the company would inspect all toilet seats 3 or 4 times a day which was being implied. This is the area that requires attention from the legislators as this is the reason we are getting tied up in paperwork and red tape to try and ensure as much evidence is provided to win a claim as it is so expensive to fight it in court.