Over the years I've attended many skirting jobs like this.
Most people think that putting some skirting down is just a couple of cuts and some glue but there's a lot more to it, especially when floors are uneven and there are corners not true, think boxed pipes.
My prices reflect that, but for some people it's too much.
Then they call me back to rectify and the price is even higher because of the removal, glue scraping, cleaning and more material.
If I was you I would give the installer the option to reduce the bill and I would do the skirting myself.
It will take longer, but it would be done properly.
As a side note, did you see them levelling the floor?
Anyone who has used levelling compound a couple of times knows how to get a perfect or near perfect finish.
Those large gaps are an indication that either they never levelled a floor before or they didn't bother altogether.