The current rules covering Holiday Accommodation (including Hotels and AirBnB type places) are in The Health Protection (Coronavirus, Restrictions) (Steps) (England) Regulations 2021, you can see the list at https://www.legislation.gov.uk/uksi/...1/paragraph/12

Based on my experiences of travelling for work, most hotels do want some bit of paper, but they generally ask too many questions about the detailed reasons given, as long as the general name + dates + overall reason are listed.

If your builder writes you a note saying they need to make the house temporarily unhabitable for a few days due to work, you should be fine. If you have something from the builders saying they are going to be making lots of noise and advise everyone present to wear ear protection, coupled with a letter from work saying you're needed on calls, again I'd think you'd be fine.

Overall though, if you ring the hotel you're planning to stay in, say you're planning to stay due to building works making it not practical to stay home, and ask what paperwork they'll need, you'll get a better property-specific answer!