Industry tags are read off a company's website. That works beautifully for a company with a website, and tells you nothing about the millions that don't have one — the small contractor, the care home, the local haulier, the single-site manufacturer. They are often exactly who you want, and they were the hardest to find.
Those companies do carry a classification: the one their own registrar or statistical office gave them when they registered. You can now filter on it. Open "More filters" in company search and look for Official classification code.
Type a number or an activity — 62.10, 6210 and "software" all find the
same thing — and pick from NACE, UK SIC, NAICS or ISIC. 15 million companies
in the database carry one of these codes: 9.4 million NACE, 5.3 million UK
SIC, 611 thousand NAICS.
A code also matches everything beneath it. Pick a division like 62 Computer programming, consultancy and related activities and you get every class inside it, not just the companies filed at that exact level. So you can start broad with a sector and narrow to a four- or six-digit class when you know precisely what you are after.
It sits alongside industry tags rather than replacing them, because the two are good at different things. A tag is one vocabulary across every country, so "dental practice" means the same in Norway and Florida. A code is the authority's own and is only comparable inside its own scheme — but it exists for companies no classifier could ever read. Use tags to describe the kind of business you want; add a code when you need the register's own answer.
Everything here is on the API too: stat_codes=nace21:62.10 on the company
search endpoint, with /api/v1/discovery/stat-codes/?q= to look a code up.