Anything with a sharp point or blade, except for folding knives with a blade less than 3". I think a fixed-blade knife of any length is forbidden, if I read this right, unless you are a Scotsman in a kilt with a dirk, or a Sikh with a dagger in your turban.
http://www.opsi.gov.uk/acts/acts1988/Ukpga_19880033_en_12.htm#mdiv139
139.—(1) Subject to subsections (4) and (5) below, any person who has an article to which this section applies with him in a public place shall be guilty of an offence.
(2) Subject to subsection (3) below, this section applies to any article which has a blade or is sharply pointed except a folding pocketknife.
(3) This section applies to a folding pocketknife if the cutting edge of its blade exceeds 3 inches.
(4) It shall be a defence for a person charged with an offence under this section to prove that he had good reason or lawful authority for having the article with him in a public place.
(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—
(a) for use at work;
(b) for religious reasons; or
(c) as part of any national costume.
(6) A person guilty of an offence under subsection (1) above shall be liable on summary conviction to a fine not exceeding level 3 on the standard scale.
(7) In this section "public place" includes any place to which at the material time the public have or are permitted access, whether on payment or otherwise.
(8) This section shall not have effect in relation to anything done before it comes into force.
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And you can't advertise or market a knife or pointy thing as being suitable for combat:
2. - (1) A person is guilty of an offence if he publishes any written, pictorial or other material in connection with the marketing of any knife and that material-
(a) indicates, or suggests, that the knife is suitable for combat; or
(b) is otherwise likely to stimulate or encourage violent behaviour involving the use of the knife as a weapon.
(2) A person who is guilty of an offence under this section is liable-
(a) on summary conviction to imprisonment for a term not exceeding six months or to a fine not exceeding the statutory maximum, or to both;
(b) on conviction on indictment to imprisonment for a term not exceeding two years or to a fine, or to both.
http://www.opsi.gov.uk/acts/acts1997/1997021.htm#6