UK: Computer controlled wood milling machine advice required

I have to construct a few hundred hollow hardwood boxes. These are to be open on the underside with some detailed but shallow carving on the

I am looking for a service in the UK that has a computer controlled machine to mill such an item from a solid hardwood block.

Does this seem like a sensible approach to make the item? Can anybody recommend a UK service that can carry out this task?

Thanks,