It is likely that councils will happily listen to any comments/requests you may have, and some may offer a choice of features.
In most circumstances it is unlikely that you will be able to choose the variety of tree, this is because the selection of tree has to be made based on the circumstances of the location it is being planted. Factors include, what type of trees are already in your road, whether you are in a subsidence risk area, the width of the road and proximity of houses, along with consideration of the existing mix of tree species in your borough.
Trees for Streets run street tree sponsorship schemes on behalf of local councils. It is up to your local council to determine the detail of their local scheme, including whether to offer residents the choice of tree.