Tighten the locknuts against the cones, leaving a little bit of play (sounds like that's what you have, but just double check the locknuts/cones are tight to each other first).
Then get a spanner on each locknut and tighten them together ever so slightly. Check for play in the axle. If there's still play, tighten the locknuts down again, a little bit at a time, checking after each time until there is no axle play.
If you do this and it still feels like it's blinding then you might have a bent axle.
Tighten the locknuts against the cones, leaving a little bit of play (sounds like that's what you have, but just double check the locknuts/cones are tight to each other first).
Then get a spanner on each locknut and tighten them together ever so slightly. Check for play in the axle. If there's still play, tighten the locknuts down again, a little bit at a time, checking after each time until there is no axle play.
If you do this and it still feels like it's blinding then you might have a bent axle.