The BBC isn't allowed to run ads either. They are also generally can't recommend products without talking about alternatives. Always amusing on kids arts/crafts shows when they name a brand and then have to state other products that are available.
They can display adverts under certain circumstances though. Public billboards aren't censored in news reports, and adverts on the sidelines/stands of sporting events (like football) can still be seen.
It's only a requirement for content served inside the UK though; international content (such as BBC.com) is allowed to (and sometimes does) show ads because it's technically not covered by the licensing agreement for the UK.
They can display adverts under certain circumstances though. Public billboards aren't censored in news reports, and adverts on the sidelines/stands of sporting events (like football) can still be seen.