Trains can turn around at all sorts of locations, including London Bridge, St Pancras and within the Canal Tunnels. You don't need sidings to terminate a train, and storing them is less of a problem than getting them out of the way to start with. Plus ideally you need a driver to spin them round and take them somewhere useful straight away, otherwise you've later got to a get a driver from a driver depot to remove the stock.
Even if you had sidings, you'd either not have drivers competent to actually drive into them, or if you did, you'd quickly fill them up with displaced trains.
The problems are often coming from a sheer lack of drivers being available at locations where the trains can't easily be disposed of anyway. It's virtually impossible to do anything if a train turns up at (say) London Bridge and nobody can move it forwards to a sensible place, and if the driver can't return the other way (the original pilot driver has disappeared / no hours within the duty to return the opposite direction / another train waiting immediately behind / etc.) then you're going to wait a while anyway.
Better planning is needed so that if a pilot driver becomes displaced during their duty, the main driver is able to turn the train round in good time or another driver can be sent out to take the train back in the opposite direction. Good luck with that at the moment...