Although we are now in to our third lockdown in England, business do not have to put everything on hold as they may of during the first. The first time we went into lockdown it was very new and strange for everyone and the rules were even stricter than they are now. Many companies and individuals have adapted their businesses to allow them to continue working during these tough times and they have processes in places to allow for minimal disruption during periods of tighter restrictions.
If you were or are in the process of having a new website built or a redesign of your current site then you should try and continue with this as much as possible. Many people such as in the web design and programming industry, can easily work from home, so they unless they are ill, they will probably be happy to still continue working. This may be the perfect time to work on a new site as hopefully it will be all ready to go for when restrictions start to ease. It will also give you the opportunity to iron out any issues that may arise when the site is first launched.