Depends what you mean by small tree ... On the 2m side Pittosporum and dwarf acers come to mind though others may suggest more. Hawthorns and related creteagous on dwarf stock at 3m max also have shallow root system though the tap root will go down a long bit!! Birches are shallow though wide rooted. Tree mahonia roots are compact but very deep.

Thanks. By small tree I meant for them to mature no more than 3m high.

The only other thing that springs to mind are the creeping conifers - lots of width but less depth - dwarf stock prunus and any of the dwarf stock fruit trees. Birch already meantioned above. Willow suffer badly when the water table drops, so could be another. Most conifers are used to a high water table, so could also be another.

Thanks again, much appreciated with your response.