Q. Hard lines are the walls on the first floor underneath, joists on the first floor landing run left to right so does that mean the central wall running front to back is 'load bearing'?
If your house is in the UK (which I'm guessing it is), then without a doubt the central wall running from front to back is load-bearing.
Q. Initially I thought of putting 8x2s front to back, supporting them on internal walls where possible. Problem is that the angle of the eaves would not allow me to rest the ends on anything substantial so could I just bolt them to the rafters as long as they were supported by the walls downstairs too?
Refer to this question here on SE, and read all the answers and comments found within.
Running parallel to the existing ceiling joists is the easiest and preferred way to go.
Removing the binders "locally" to allow the new floor joists to pass is "normally" considered acceptable (then connecting/pinning them back to the new joists passing through), though you would want to check such a detail with your local Building Authority before doing so.
Otherwise if you go the other way (perpendicular), you end up going above the existing ceiling joists, which causes a major re-work of the existing wall plate area that sits on the exterior wall and the roof area above.
Q. Then I got thinking that I'd need to go left to right .. a) because the load bearing walls go down the centre of the house and b) because if I don't the ceiling binder will be in the way. Same problem however with regards to getting the joists to sit on the external walls and I'm guessing I'm not allowed to bolt a plate to the chimney wall and hang things off that.
Whatever you do, do not connect anything to the chimney wall. Doing so is an absolute no, no in the UK (if I have your location correct).
Again, refer to this question here on SE, and read all the answers and comments found within.
Of course another option is to remove the existing ceilings (lath and plaster), binders, etc. Leave the existing ceiling joists and install new appropriately sized floor/ceiling joists parallel to the existing, then fix a new plasterboard ceiling to the new joists. Granted, such an option adds considerable mess to the job, and a reasonable cost increase.
You are correct, the ceiling material provides a bracing effect for the joists. This is more critical on the compression (floor) side than the tension (bottom) side. There are specific ratios of joist width to height ratios based on span length where bridging or solid blocking must be installed.
I am sure 2x8 floor joists do not meet this criteria. You do not need bridging or blocking. You will actually get more creaking with bridging or blocking installed due to the extra joints rubbing under joist flexure. Of course, these are the innocuous flooring type creaks and not the ominous splintering sound of impending failure.
Best Answer
Unless you have a big ridge beam you failed to mention, this is a brilliant piece of misdirection. While superficially correct, what do you suppose would happen if the walls were not tied together? The roof would collapse under it's own weight! No snowload required.
The lateral force exerted on the walls from a low pitch roof is substantial. While it is possible to stabilize the roof with collar ties alone, the end connections become very critical in low pitch applications. You'd be much better off with a high pitch roof in terms of spreading forces from the roof.
If you're going to do a major structural change anyway, I would install a ridge beam along with proper end supports in order to achieve maximum openness from my efforts. Regardless of which approach you select, for any major structural change you should consult with an engineer to ensure everything is done safely. Small details can make a big difference.