planting in between tree roots

[NotAnEMERGENCY]

I would like to plant up the area between the two birch trees. They are well established trees - maybe 10 metres tall? Will the roots cause problems if I start digging up the soil to plant other shrubs? Will I be able to get enough 'access' to be able to dig a decent sized hole for planting?

I meant to add a photo! Trying again...

Grrr - it's not letting me. Anyway, the trees are about 1.5 metres apart in a border that's about 1 metre deep.

I used to have 6 birches along the boundary of a garden. Some plants did well, hebes, Japanese anemones, quince Japonica, crainsbill geranium, loostrife, and asters. Spring bulbs did well, as it was a type of woodland setting.
General digging was impossible so planting involved digging in pockets between the roots.

I don’t think the beech trees will be too bothered by plants near their roots, it is the plants that will have the problems. Have you thought about what plants you want to grow there? You need plants that will thrive in dry shade. Have a look on the Beth Chatto site, there is a really useful screening tool you can use to find plants for different conditions so they at least get a fighting chance!