The police pretty much have a veto over allowing football matches but I'd be very surprised about them having much say on engineering works.
Writing as a football fan, I think it has to be on the leagues, clubs and FA to work around engineering if necessary and not the other way round. Football matches are unpredictable beasts: they're subject to postponement based on progression in different competitions, subject to quite significant variations in attendance based on success of a club or popularity of a manager/owner, and their relative importance is unpredictable, particularly in the latter half of the season. Their impact is very variable too: 17,000 people attending an event in London is not that remarkable, but it can overload a smaller town or a place at the end of transport networks, so any fixed set of rules for matches is hard to implement. Football matches are quite flexibly scheduled too: for a club in the Championship with a 46 game season, there should be sufficient flexibility to arrange matches in a way to avoid most clashes with other events or engineering work. They can be moved between Saturdays and Sundays if needed, and there are many vacant midweek slots in the season too.