TL;DR — There is no credible evidence to support this claim.

Howard Wilson was the leader of Labour Party from 1963-1976 and during that time was Prime Minister twice. Yet, his time in politics was clouded by unfounded accusations of his being a Soviet spy. This theory came from Anatoliy Golitsyn, a Soviet defector but can also be linked to [his pre-politics connections with businessmen in eastern Europe and contacts at the KGB] (https://www.townandcountrymag.com/society/tradition/a29213646/prime-minister-harold-wilson-facts/).

MI5 kept a file on Wilson through out his time as an MP but no evidence was acquired that supported the accusations made against Wilson. Golitsyn was labelled an ‘unreliable conspiracy theorist’ by Christopher Andrew, the official MI5 historian.

In sum, there is nothing to suggest that Wilson was a KGB spy. The accusations can be linked to his left wing politics and his previous work in eastern Europe.