A semi-outsider's perspective if I may...
It's clear even to the casual observer that BA's threats are an opportunistic attempt to dramatically worsen T's&C's across the board. They're banking on this working because:
1. The unions are pretty powerless in these circumstances - striking would be a minor inconvenience to BA at worst
2. The public, and politicians, are distracted and they won't face the strength of scrutiny that they might usually do if they attempted something like this
Frankly, there's little anyone can do about point 1 until there is a major recovery in air travel demand. In other words, the war (and I would take BA's letter as a declaration of war!) will be won or lost by the ability to get public and political support.
BA's one weakness here is that given a long enough downturn, they will require government support of some kind (above and beyond the furlough scheme). In fact, IAG have already blinked slightly and weakened their position by accepting the spanish government loan, highlighting their hypocrisy to the more observant MPs.
Government support will come with conditions, which may be the only route to protecting jobs and conditions, so it's crucial to have MPs advocating your side of the argument at that stage.
Direct appeals to MPs are definitely worthwhile - I'll be sending a letter myself in support - but in order to have any chance of a successful outcome, you'll need to win the support of the media and public in general. Pressure from the media in particular is probably the most powerful influence on today's politicians. Here's where you need to be very careful - pilots, BA pilots in particular, are not the easiest group for the 'man on the street' to sympathise with. Don't shoot me! IMO the responsibility and technical demands of the job justify the salary, not to mention the training costs and nasty hours. However, compared to many other careers which involve high levels of responsibility, academic ability and lengthy training (e.g. Engineering, Medicine, etc.), you have an objectively good deal. Again, that's not a criticism - well done for protecting it better than many industries - but it does mean that in order to appeal to the public sentiment, some humility is required. I'm not sure the whole 'home counties' soliloquy is quite going to hit the right notes!
I'd suggest the following might be constructive:
1. A very public offer from the unions of dramatically reduced salary (50%+?) & part time arrangements for perhaps 6 months in return for no forced redundancy. If BA's real motivation was to reduce staff costs to get through the crisis (it's obviously not!!), this would solve their problem. OTOH, their refusal of this offer would confirm beyond any doubt their nefarious motives. A big price to pay on the off chance they did accept but nothing compared to the job losses & T&C decimation suggested
2. Unity within the BA pilot community - bickering about who is being more selfish by keeping their job isn't going to help anyone - you're all getting rodgered at this rate!
3. Working with other departments - don't forget that CC, Engineering and others are going through the same as you at this point. I know the relationship has been a little acrimonious at times, but you're in this together, and will only be able to get out of it together. CC in particular may be a useful ally - their plight might be an easier sell to the tabloids.
4. Work with the rest of the industry - Somewhat ironically, it may be very much in your interests for Virgin to get the loan / bailout they are seeking. It would effectively force BA to do the same, and as mentioned above, this is the opportunity to enforce conditions on job retention & protection of T&Cs