It depends. It is lawful if one has a lawful reason, such as it's needed for work, or it's a folding pocketknife (e.g. a Swiss Army Knife) with a blade less than 3 inches.
The primary legislation is s.139 of the Criminal Justice Act 1988 which makes it unlawful to have in a public place:
(2) ... any article which has a blade or is sharply pointed except a folding pocketknife.
(3) .... [this includes] a folding pocketknife if the cutting edge of its blade exceeds 3 inches.
Subsection (4) gives the "good reason or lawful authority" general defence for possessing such an article which is complemented and supplemented by:
(5) Without prejudice to the generality of subsection (4) above, it shall be a defence for a person charged with an offence under this section to prove that he had the article with him—
This site gives some more information and identifies certain knives that are banned, and this site, under "legislation", lists semi-related offences.