UK unions lost their power during the seventies and early eighties when their myopic vision lead them to pick the wrong fights. They tried to resist change when it was obvious that the industrial landscape was in turmoil. In trying to resist change they made UK industry unreliable and expensive. Customers went elsewhere and the so did the jobs. In resisting change the unions doomed the companies that provided their members. The unions lost their muscle and to a large extent their relevance to UK industry.
Behind this was the desire of the unions to direct the political agenda. Challenging the government ensured that legislation to curb the power of the union barons was enacted.
I guess the short pithy reason would be the lack of foresight on behalf of the union leaders of the seventies ensured the demise of the unions in the UK