Hi S1m, I worked most of it out, but it's always best to check, and never make assumptions. Having Pic 2 being unrelated to the others, required some clarification.
I reckon the bay is only on the ground floor, and doesn't go up to the second floor (hence a 2 storey bay) which would mean there's a lot more weight on the foundations. With a single story bay, you could just take down the bay, and brick straight across as a cheap option, but you'll want to retain the character, so that'd mean underpinning to stop the bay going out any further. You could then tie the bay into the front wall, but that'd be putting a bit of a strain on it, and it's not something I'd opt to do.
Underpinning a bay isn't difficult, you've just got to dig down in sections, and drop some concrete in, then move onto the next section.
Or you could also take the bay down, do the foundations properly, and then rebuild the bay.
But it's pic 2 that determines whether you need a surveyor, as it's also cracking, and may well be a problem that's been covered up already. Is the render on the other houses in the street in the same places.