Murphy's is a reputable and national company, they'd probably make a much better job of it than the council. Couldn't you write and tell the council that you have an independent quote of £500 and apply for permission? Or, if this was a "job on the side" and wasn't going through Murphy's books, you could have it done and deny all knowledge, telling the council you thought they'd just kindly decided to do it for free. They have no proof of either you or Murphys being involved... that'd really annoy them

And it'd be far more expensive for them to pursue the matter than it would to just leave it, after all, it's cost them nothing either.
If ever I was drawn to use "the worst word of all", I would reserve it for describing city councils. The way they fritter away our money* on ridiculous, wasteful, shortsighted schemes is a total disgrace. The dilemma is that in order to change it, we need people with an ounce of common sense to get themselves in there - unfortunately, no person who meets that description ever would.
*I say "our money"... being a student who doesn't pay tax...! But I will, one day...