^^Ah, OK, not a cottered crank then.
You really need a hexagonal socket to tighten those bolts down pretty tight to press the crank firmly onto the spindle so it won't wiggle loose again. A socket will engage all six flats on the bolt and allow you to turn it with the required force without slipping off and marring the bolt. Bike shops sell wrenches (spanners, I think you call them in the U.K.) made just for this purpose. But if you have a set of sockets with a ratchet driver, the 13 or 14 mm socket will often work. Only trouble is, often the walls of the socket from the ratchet set will be too thick to allow the socket to slip down into the cavity in the crank to grab the bolt.
As other posters have mentioned, when a crank comes loose like this, the steel spindle often damages the square hole in the crank so that it will not stay tight, or continues to wiggle even when the big bolt is tightened up fully. Then you need a new crank.
First lesson in Mechanics 101: Never use any kind of grips (pliers) on a nut or bolt. They'll ruin it so that a proper wrench (spanner) will not fit to do the job right.