Our soil is very poor quality and very dry in eastern England. I keep finding a web of roots which don't appear to be attached to anything but where found soil just exceptionally dry poor quality and sometimes a white type ash also in the soil. Any suggestions how to improve soil or how to get rid of this root mass.

The roots are probably from a tree. Tree roots can easily extend twice the height of the tree.

The soil may be dry now, but that's probably not the case during winter.

Those unattached roots might be mycelium.
Not harmful...
Here's an explanation:
https://insteading.com/blog/my...

Yes, it could be mycelia. Easy way to tell between root or mycelia:
- roots are strong and varying in diameter, usually brown or dark brown except near the tips.
- mycelia are usually light colored or white and have no strength, as there is no need for it

it's possible that the "white ash" could be dead mycelia.