The source of the water was coming from the side of the wall, where you can see the rotten part of the joists. This was caused by the groundworks outside being higher than the level of the external wall DPC.
I excavated the ground to around 70cm deep, poured in some concrete to below 30cm of the DPC line, and backfilled with 20mm shingles to below 20cm of the DPC line.
There are times when the water table would be high, and this was penetrating the DPC, The party wall on my neighbours side, also has rising damp; its condition is worse than mine.
When we removed the joists, we had to replace some of the subfloor as it was rotten and wet. The subfloor rubble had been damp too; since the repair, I have been testing with a moisture metre on that side of the wall, and it's within the limits.
There is sufficient ventilation, as I can feel a draft, when I put my hand near the exposed part of the wall, where the side skirting has been removed.