The highway authority has a duty to repair roads. County councils, and metropolitan district councils are normally the highway authorities for their areas. The duty can be enforced through the courts, but this would take time and money. You are certainly entitled to press the highway authority to meet its obligations.
Parish or community councils may in some cases (if they have undertaken the duty or made representations to the main highway authority) be responsible for the maintenance of highways within their district. This would involve delegation from the highway authority; so far as I know, a parish council has no power (apart from section 137) to maintain roads.
Working on roads without the agreement of the highway authority would be likely to lead to problems.