Many unions were smashed in the 80s by Thatcher and workers no longer belonged to them.
The problem was that unions - whether by design (infiltrated by communists) or accident - became increasingly militant with very little oversight. (Does anyone remember the massive open air public strike ballots they held ?).
The country was sick of strikes, (also don't forget that if Leyland workers went on strike, they were allowed to picket other companies, and stop them working).
Britain didn't get the moniker "sick man of Europe" for nothing.
(Again, betraying my incomplete Englishness here, but I never understood why unions weren't able to sit down with management and work towards a better outcome for the entire company. After all, who were the expert steelworkers, carmakers, miners, shipbuilders etc ????).
My first "real" job was with a just-privatised utility in the 1980s. The week I started they had rearranged the offices to provide a mock up of a project that was being delivered. All the desks had been moved around. Friday afternoon, when the demon was finished, I asked where I should move my desk. There were audible gasps of horror, and my boss gently took me to one side and warned me not to even think about moving anything. That was the job of "house services" and if they found I had moved a desk (or my chair) they'd be out on strike. "Again" as she put it. A couple of hours later they turned up and did the move. (Which had been booked 2 months earlier). As far as I could see the only thing they had that I didn't was a brown coat.
Demarcation anyone ?
Interestingly enough, this privatisation happened the time "insider trading" became a thing. Rather heavy handedly, the company overseeing the share sale decided unilaterally that entire swathes of employees would be subject to a check process if they wanted to sell their shares. A check process which meant you had a 2 week delay on the price you got. The department I was working for was included as we had access to very price sensitive data which could affect the share price. The problem was our bosses were not subject to the same rules. Which - as the unions pointed out - meant they could request the data from us, and then make trades themselves. The union (NALGO !) got involved, and I briefly had to cross a picket line. I didn't join the union as I was only there for a year.
My memory of Thatcher and the unions is that if she set fire to them, it was only after they had stacked themselves into a neat pyre and poured petrol on themselves.
When my Dad started work in the 1960s, "foreigners" weren't allowed to join the union. One of the reasons he had lots of Indian and Caribbean friends at work.