The Flying Pickets were actors coming from John McGrath’s 7:84 company (7% of the population earn 84% of the wealth) but also political activists who had been active in the 1972 and 1974 miners strikes. The flying picket, outlawed by Thatcher, was an age old industrial tactic of moving from workplace to another to shut it down and bring the workers out on strike.
While the NME interview brands the song as a novelty hit it was just three months until the 1984/5 miners strike where the flying picket- Orgreave-played a central role.
Only You was top of the singles charts throughout December 1983
The Top of the Pops performance is here
The lead vocal is from the sadly late Brian Hibbard
Kmflett's Blog 
The Flying Pickets: how we made ‘Only You‘
Getting the Christmas No 1 was a big deal. We did Top of the Pops dressed as snowmen and somebody told us it was Margaret Thatcher’s favourite record’
https://www.theguardian.com/music/2019/dec/17/david-brett-rick-lloyd-how-we-made-the-flying-pickets-only-you