Adding pillar to existing wall

[Rocket01]

I have an existing garden wall between myself and next door, it's solid and stable enough but there are cracks down the mortar roughly every 2 metres, having peeked over the neighbours side there are no pillars along the length of the wall only at one end (it ties to another wall at the other end.) As it's my responsibility, would it be possible for me to remove the mortar, take out the blocks and tie in a couple of pillars every 2 metres or so?

 

[^woody^]

What problem are you trying to solve? That cracking may well be from nothing to do with lack of piers.

And widening the foundations for the piers too?

 

[Rocket01]

Yes I'd be adding a foundation for the piers, the cracking is down the length of the mortar and through both sides of the wall, I'm worried that it may not take too large a gust of wind or something for the wall to come down, I have a young son and the house next door is in the process of being bought by a family. I just want to make it safe.