They were doing in the 1970's what they had and have done all their existence - looking out for their members' interests. It's as I say a myth that they were running the country. They weren't. Heath didn't need to call an election but he did and lost. Callaghan should have called an election in 1978 but he chickened out. He had a fair chance of winning in 1978, and had he done so would have had a mandate to impose his pay policy. he didn't and the rest is history. The "winter of discontent" followed - it was a bad winter - a bit like the one we're just coming out of - but it wasn't as bad as the press portrayed it - but then as I said in another post the British press are like that.
The miners, in 1984 misguidedly under Scargill came out not for more money, not to bring down the government, but to protect their jobs and commuities. Thatcher used every trick in the book including some that it now seems were against the law to defeat them. She won, but the bitterness is still there in Cas, and Fev, and Grimey, and Hemsworth (where my own family are from) and one day it'll turn and bite someone.
I just want to pick up on that first point about "looking out for their members' interests". At that time, the unions were very highly focused on pay and there were regular strikes for increases. I don't believe this approach really is "looking out for their members' interests", at least not in the longer term, broader sense of "interests".
My own recollection of the times is one of intransigence. Management (and most of the problems were down to p***-poor management) and unions would face off across the negotiating (sic) table and refuse to budge. Broadening the scope of the discussions might have led to better industrial relations and practices. I always wanted to bash their heads together, personally.