There is no published literature on this particular case of lexical variation.
Pumps and plimsolls are by far the most popular choices, making up a massive 97% of responses. Pumps is more widespread throughout the UK, but shows clear prominence in the North, whereas plimsolls is favoured in the South. Daps is an interesting lexical choice, as it shows a very specific concentration in the South West (including the southern coastline of Wales). Bristol and Cardiff, on either side of the Bristol Channel, seem to be two hot spots for this word. This likely stems from the fact that the Dunlop Athletic Plimsoles (DAP) factory was based in Bristol; it’s possible that the general term daps emerged from this brand name.