For a problem with a commonly shared drain in my neighbour’s garden a few years ago, after they received the call, Thames Water’s inspector arrived reasonably quickly.
It went wrong from there. He turned up when no-one was in, drew the wrong conclusions but did actually instruct his contractors to attend. Contractor duly turned up but declared he could not raise the double seal cover and left site.
On returning later that day I released the cover after a few minutes effort and got hold of the inspector once more and pointed out to him that TW had to do better and that we needed a gully sucker to clear the surcharge and remove the blockage.
He was a bit miffed, returned to site pdq and then ordered the gully sucker. Overall there was about 26 hours wasted.
So prompt response when there is an emergency but a close eye is needed on their actions and proposals.