While the word 'soccer' was widely used in the UK and Ireland while I was growing up, it tended to be used by 'quality' newspapers in the UK, and its purpose was to distinguish proletarian association football from rugby union football, which was played by the wealthy. My conjecture is that if you screened for usage rates of 'soccer' vs. 'football' by the Times and Telegraph, on the one hand, versus the Mirror and Sun, on the other, you'd find big differences. In Ireland it was somewhat different; we used 'soccer' to distinguish the game from Gaelic football. The working class in Britain just called soccer 'football'.
As the British boomers grew older and adopted leftish views, in a sort of inverted snobbery that's particularly common in the UK, they rejected their parents' 'soccer' in favor of 'football', as they embraced the egalitarian association football and rugby union became stereotyped as a game played by rich thugs. Now the word 'soccer' is associated with America and is rejected even more vehemently by these same people, but in 1980, when use of 'soccer' in Britain began to decline, nobody knew or cared much about American sport, or what words they used to describe it. It's only with the internet Britons have become so conscious of American usage.
So while the author's data on word usage are invaluable, I think his explanation is somewhat off-base. 'Soccer' iniitially became unfashionable in the UK for an entirely different reason.
Oh, and a belated h/t to Roger Pielke Jr. for tweeting the link to the piece.