They might not hold so much political influence now but they still have the power to strike and bring a company to its knees, you must have been following the BA - Unite saga over the last few months, The Unite union has nearly 2 million members according to their website and they make good sized donations to the Labour party as far as I know.
You refer to the 70's when they had much more influence, as far as I have read and heard that is true and from what my Dad has told me they pretty much destroyed British Industry because of strikes for higher pay etc which companies couldn't afford, British Leyland was very badly affected by the strikes I think (probably didn't help that it was too big a company, too many divisions, and had some financial difficulties, think it split into quite a few companies after that?).
The BA strike in my opinion is ludicrous, yeah BA might be cutting some jobs around 4900 in total I think and quite a lot were voluntary redundancies or reduced overtime, BA needs to cut costs like every other airline around the world and the cabin crew want to strike (They were going to over Christmas disrupting travel for millions, but the High Court found it illegal based on how the balloting was done) do they want BA to turn into what Japan Airlines has 16,000 workers sacked (1/3 of the workforce) declared bankrupt and all it's shares worth less than a Boeing 747, yeah it might be horrible that jobs are going but millions of others are affected around the world, but if BA wants to continue running and be a significant player in the Air Industry they need to cut costs to maximise profits and clear debts which number £600m, $200m and €300m (BA site on there debt - http://www.badebtholders.com/phoenix.zhtml...rol-debtsummary
) no other way about it with low passenger numbers.
If I was the BA chief executive I would call the bluff of the cabin crew if they want to strike and try running the company into the ground by demanding better pay and less job cuts, when BA as a company can't afford it if passenger revenues don't rise then sack them I can guarantee there are plenty more people out there who would kill for a job and pay, you all might think it is harsh but if they are going to play hard then you have to do the same if negotiations aren't working which in this case they don't seem to be.
I don't know if I'm reading into things wrong here but that's my view of it, not fully sure about the 70's stuff since I was born in 91 so someone else might see that different and be able to correct something or add more detail.
But overall I probably agree with Groovicus on this it raises costs too much and makes it so that those who can't do their job properly get a job where as someone who could do the job better doesn't because they can't sack/fire the worker there, although the company would most likely hire the better worker when they first look for someone to fill that position.