Yes there is plenty of space BUT taking Little Cheyne Court as an example the land is actively farmed pretty much right up to the base of the turbines. (see the pics below). So to add a "standard" container sized battery pack to each turbine would encroach on that farmland, if using Tesla Magapacks (30ft long, so 3/4 the size of a standard 40ft container) then you would need additional space around them for security fencing - you can pretty much access all of Little Cheyne Court on foot or even drive up to them along the farm tracks. I can imagine a lot of opposition down here to adding that to each turbine. Then each one (assuming Tesla Megapack ) is just under 4MWh capacity. The turbines on that site are rated at 2.5MW so a couple of hours and the pack is charged. The flip side is, a couple of hours and it is discharged. Yes it will increase utilisation but I see the biggest issue as long term storage where we have low wind for days - battery storage, pumped storage is OK for a few hours to help ride peak demand but not longer periods and I see nothing viable on the horizon, certainly not at the scale needed. "small" battery packs at a wind (or solar) farm are not going to solve that one.
Mounting batteries in the turbine tower sounds a good idea but I think is a non starter - too many different designs, access problems and also towers are not designed to support the massive weight of batteries - though I suppose they could be.
