Many thanks for the suggestions.

Looks like a pair of battens is in order, one underneath to take some
of the weight of the units, and one set at the height of the unit
brackets. I may still use anchor fittings on the upper batten.

It is interesting to me that so many of these 'diy' cabinets use fixed
position brackets when partition walls and plaster board are so common
- the odds of finding a stud are not good... I'm also surprised that
there seem to be no specific products available to suit this task
(perhaps a long metal bracket with movable hooks for modular
cabinets). Still I may fashion my own!

Thanks again.