The City’s website provides an excellent explanation about noise nuisance and what their Environmental Health Officers can do for you. I only hope their actual response is as good.
The website page (at the time of writing this) is https://www.cityoflondon.gov.uk/business/environmental-health/environmental-protection/Pages/Disturbed-by-noise.aspx
You should also read https://www.cityoflondon.gov.uk/business/environmental-health/environmental-protection/Pages/Construction-.aspx on construction work in particular.
The crucial point is that the EHO will only take action if they witness the noise themselves. This is what they say about response time: “If the noise is happening NOW, you should be contacted within 45 minutes (8am to 5pm) or 15 minutes (5pm to 8am). Where noise is ‘happening now’ and the responding officer assesses a visit is necessary, we aim to visit site within 75 minutes (8am to 5pm) or 60 minutes (5pm to 8am) of receiving the complaint.”
So, complain first thing in the morning when jackhammering starts. If you complain at 3 pm, by the time anyone gets to you, the builders may have packed up for the day.
And may I also suggest, don’t tell the builders you are making a complaint, or they may cleverly become Trappist builders for the day.