Nest sites are protected. Not sure if the work is going to be disturbing the nest though, based on what you have written. Presumably, they have given some sort of notice period. Wouldn't that take it past fledging stage?
nesting birds are protected and ideally work needs to be done when the birds have fledged and nesting season is over. just check the timings on the work planned.
www.gov.uk/.../wild-birds-protection-surveys-and-licences
www.gov.uk/.../wild-birds-protection-surveys-and-licences