Can anyone please advise if there is a way to contain the roots, so
that they will not spread any further ? Does keeping the branches well
trimmed force all the growth back to the branches, rather than the
roots ?

Pruning a tree will in general prevent the tree from sending out quite so many
roots, though the success of this is limited. As for containing the roots,
forget it. Slabs will not contain the roots of a cherry tree enough to
guarantee that no roots will cause damage. Also be aware that any drains that
may run through your garden may be subject to 'attack' by roots of cherry
trees.

Hope this helps.

Dave.