Is the spindle sliding along its axis? If so check the LH crank is properly attached to the spindle: unscrew the small pinch-bolts, tighten (gently) the wide fixing bolt that pushes the arm onto the spindle, and re-tighten the small bolts.
The wide fixing bolt needs a special tool, "TL-FC1":

If that doesn't help, remove the crank completely: remove the 3 bolts mentioned above, pull off the LH crank arm, and slide out the spindle with the RH crank. Check you have all the appropriate spacers by comparing with the diagrams from Shimano Techdocs: Double, Triple, Compact

Once you have removed the cranks the state of the bottom bracket will be clear. If the cranks are ok but you're getting 1-2mm of movement, either the threads or the bearings of the BB must be utterly shot.

Before reassembling the cranks, ensure that the splines and spindle are impeccably clean and given a thin coat of fresh grease.