Refer to the diagram supplied:
We say that it is because of change in column height that causes osmosis to stop.
But, doesn't osmosis stop when concentrations of solutions are equal?

And if atmospheric pressure were not to be present, would the level go up higher or not?

No. Look at your diagram - if the large container were a thousand times greater in volume, the water would still rise to the same level in the inner tube. Would the concentration of solute in the outer container change much? If the concentrations become equal, solvent flow will stop, but that's not the usual case.
Because the difference in height is small, the atmospheric pressure on both surfaces is assumed to be equal, hence there is no effect on height.

So it is atmospheric pressure which is stopping osmosis but solutions still don't manage to have equal concentrations?
Thx for your help

NO. Atmospheric pressure has nothing to do with it. The omosis stops when the pressure (the "head") is sufficiently large to equal the osmotoic pressure. Atmospheric pressure is equal on both solutions and cancels out.