Should I use soil from under a huge beech tree in my veg plot?

Hi

My quest to improve the clay soil for my new veg beds (and in my polytunnel) continues.

We have a humongous beech tree in our garden. I don't think the ground beneath it has been disturbed for years. Very little grows - I guess on account of the lack of light - and there is a carpet of leaves, nut shells, and twigs.

Have I potentially got my own supply of leaf mould, or at least decent soil, here? I thought perhaps from the years of leaves, shells, etc breaking down that the soil beneath could be good to transport over to the veg beds and polytunnel? Is this something people with the same option do or are there reasons why it wouldn't be such a good idea?

Sorry for all the questions... I'm trying to make the transition from being green to being green fingered

Cheers

A few photos to help visualise:

 

The tree will have probably extracted most of the nutrients that have leeched into the soil, making the soil a no but the leaf litter would make an excellent soil conditioner.