Broadly true. It surprised me that the punishment isn't jail time, but you are entirely correct. The Representation of the People Act Section 61 (2) (a)
A person shall be guilty of an offence if—
(a) he votes as elector otherwise than by proxy either—
(i) more than once in the same constituency at any parliamentary election, or more than once in the same electoral area at any local government election; or
aaaand Section 61 (7):
(7)An offence under this section shall be an illegal practice, but—
aaand Section 169 (defining prosecutions for "illegal practices"):
Prosecutions for illegal practices.
A person guilty of an illegal practice shall on summary conviction be liable to a fine not exceeding level 5 on the standard scale; and] on a prosecution for an illegal practice it shall be sufficient to allege that the person charged was guilty of an illegal practice.
Note that you cannot win an election this way. Yeah ok, they can't identify your vote and so they can't fix what you did, but they can certainly re-run the election, and that would be the outcome of any election where the number of fraudulent votes in a constituency was larger than the winner's majority. The losing candidate would simply take it to judicial review otherwise.