Start with what the site has to do for the business, written down in a few sentences: bring in enquiries for a particular service, take bookings, sell products, help with recruitment, or reassure clients who already know you. Give every supplier the same brief, including the systems the site must connect to and who will write the content, or the quotes will not be comparable.
Then look past the portfolio. Attractive screenshots tell you about visual taste, not about whether the sites load quickly, kept their rankings after a relaunch or can be edited by the client. Ask for a live site the supplier built and run it through Google's PageSpeed Insights on the mobile setting. Ask how they handled redirects on their last redesign, and what happened to that site's search traffic afterwards.
Ask who does the work. Some agencies, of every size, pass design or development to subcontractors. That can work well, but you are entitled to know who is building your site and whom to call when it breaks. Ask too who owns the domain, the hosting account, the design files and the code when the project ends, and get the answer in the contract.
Ask what happens after launch. A site nobody looks after falls behind: plugins go out of date, forms stop sending and pages slow down as images pile up. Whether the answer is a care plan, a support arrangement or training for your own staff, agree it before launch rather than after the first problem.
If being able to sit in a supplier's office matters to you, let that narrow your list early, because it rules out remote firms like us. If it does not, widen the search: the useful test of any web agency in London or elsewhere is the written answers to the questions above, not the address in the footer.