You have a claim against whoever cut the pipe and caused the sewage backup in respect of the cost to repair and empty. Your claim is in common law nuisance and negligence
You have a claim in common law nuisance in respect of the general inconvenience.
You have a claim in common law nuisance and negligence with regard to the debris and the damage.
You have no claim because the local authority have decided to put yellow lines outside the house.
You have a claim in common law nuisance in respect of the mess being carried into the house.
However if the company were not put their hand in their pocket and let you have any compensation, you will have no option but to sue them in the Small Claims Court.
Quantifying the damage caused by the debris and the cutting of the pipe and sewage removal is easy because that is valued whatever it cost to put right
Valuing inconvenience and nuisance is not an exact science and is likely to come into hundreds of pounds and not thousands of pounds.
It’s unlikely that you would get solicitors to deal with this no-win no fee and therefore you would have to pay the legal costs of going to court. Whether you won or not would come down to the individual judge. I can see no reason why you could not win certainly on the negligence and damage issues but with regard to the nuisance, it would depend on what proof you can put forward as to the extent of the nuisance.
You have a claim to bring the compensation but it’s not an easy claim at all.
Can I clarify anything for you?