Ite larger upper pipe (1&1/2") will be the bathe waste and the smaller (1&1/4") will be the basin waste which I noticed has a rodding eye before it joins the stack.
which I noticed has a rodding eye before it joins the stack.

Yeah, the upper pipe is the bath waste.Ite larger upper pipe (1&1/2") will be the bathe waste and the smaller (1&1/4") will be the basin waste which I noticed has a rodding eye before it joins the stack.

It's really annoying that this has happened now because I'm planning on replacing the whole bathroom setup anyway, but I'm a few months at least away from being able to do that.OP,
Best practice would be to totally remove both lead waste pipes.
Remove the basin waste and the bath waste - and the lead pipes up to the external pipe boss fittings including the boss adaptors.
Replace the ped basin trap with a bottle trap - & replace the bath waste trap with an appropriate trap.
An alternative would be to tie the two plastic wastes pipes together before they leave the building?
A hired, small size platform & two stabilisers will easily give you a working height scaff tower.
The if redundant the lead over flow stub could also be removed.
FWIW:
I doubt that the basin is vented - I also doubt whoever came over was a plumber?
That would be my suggestion. There's a good chance that's where the blockage is, and if it's further along you have a better chance of rodding. You'd have a problem getting a snake round those bends even if there were no blockage. Depending on the OD you can perhaps source a compression fitting for it. There are industrial ones that cater for a range of ODs if no plumbing fitting is suitable. Replace everything between there and the sink outlet with plastic, including an appropriate trap.Before I consider that, is there any reason why I can't/shouldn't just saw off a section of the pipe below the u-bend, use some kind of big poking device to try and clear the blockage, then replace the missing section with a £10 plastic pipe?
That would be my suggestion. There's a good chance that's where the blockage is, and if it's further along you have a better chance of rodding. You'd have a problem getting a snake round those bends even if there were no blockage. Depending on the OD you can perhaps source a compression fitting for it. There are industrial ones that cater for a range of ODs if no plumbing fitting is suitable. Replace everything between there and the sink outlet with plastic, including an appropriate trap.
We don't know the bath waste location etc, so can't tell. But the problem solved now anyway.Alternatively, could you replace with plastic from the wash basin, and connect to the bath waste pipe?
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