It does sound over the top, ask your engineer if there is some reason for it I would suggest. Perhaps ask him why you can't use an off the shelf cavity wall lintel.
Was this advised by an engineer or your Building Control Officer?
Piling is expensive and there might be alternatives:
Firstly you could look at how deep a traditional strip footing would have to be based on the NHBC method in the chapter on building near trees.
If strip footings would...
NHBC give guidance on building near trees which is widely adopted. If you know the type of tree, distance to the tree and the shrinkability of the soil you can use this guidance to look up the depth of concrete strip foundation that would be required from a table.
As you are close to a large...