Saw this thread and had to sign up. I recall seeing that the site is in Norfolk. It would be use fuil knowing where in Norfolk it is. The County has a mixed bag of geology, with Clays Silts and PEAT to the west, local to the fens, Chalks and Gravels to the North west of Downham Market, then diamicton heading East, which in effect is a mixed bag of everything, laid down by glacial runoff and glaciers.
The note about the tree, felled 14 years ago an set 4 meters from the property is a potential indicator of prior movement due to shrinkage of and clays and silts (hence why its good to know the location). The ground takes up to 10 years to recover after a tree has been felled but water demand differs by species. 4 meters is very close. Was it done on advice and is there evidence of repointing on the brickwork outside? do any of the bedjoints/ perps seem wider than others or is the mortar a different colour in places.
Guttering and downpipes can be an issue, as indicated by others and I usually find more often than not that localised subsidence has been caused by a failure to maintain the rainwater goods. However, this has more of an impact on fine grained silts and sands, where the water can flow through the ground, dragging fine particles with it, causing consolidation of the supporting soils. Also, failed gutters would be expected to affect the foundation of the building, not the slab.
I've certainly had one site where the contractor didnt compact to the head of strip footings inside the building, before laying the slab. The result was a 10mm drop in the finished floor to the perimeter of the building.
Your building is 1960's. It'll have relatively shallow foundations by today's standards so I'd rule out subsidence, more because of the insurance, resale and mortgagability issues but also because settlement or consolidation are more accurate words. It's also worthwhile noting that the building is 50 over years old and the skirting looks just as old.