We are definitely not natural gardeners so any help here would be
appreciated.

We have recently had a tree chopped down in our garden and had the stump
removed. About 3 weeks later we noticed new 'plants' growing all over
the garden. We dug these up and thought nothing more of it. The same
thing happened again about 3 weeks later. Having dug a bit deeper it
seems that these 'plants' are growing from the roots of the tree that we
had cut down. I tried digging up these roots, but the more I dug the
more roots I found. It seems that our whole garden is a mesh of tree
roots and it is nigh on impossible for me to dig them up.

What type of tree was it?

Mary