Blocking above wall in the way of new ceiling
I am assuming that this blocking is help stabalize the framed wall on the basement walls.  Normally the blocking would be inside the joists so that the 2x4 is even with the bottom of the joists.  Your wall was not put up this way.

Therefore your new ceiling is that low.  You could cut out the 2x4 blocking, install like I said and add another 2x4 under all the way to the drywall and this would stabilize the wall - if done a few times per span.

However you have not much to attach drywall too.  So you would also have to add vertical blocking every couple feed and add more drywall to make this right.  If all of your walls are like this... sorry.  This is a full days work considering the drywall and extra mud and tape.  And even doing this isn't the "right" way.  Your walls should be touching the top of the ceiling for lots of reasons.