If the small ones are seedlings, you need to be on top of them and pull them out before they become a nuisance - my ash tree does that, and I watch for the babies and pull them out like weeds. As to the roots - well - it's a big tree, so the roots will have spread out as far as the canopy if not further. I don't think there's anything you can do, as the tree would be damaged by removing the roots...or you'd lose it, of course.

Your choice - a lovely tree or a perfect lawn?

Sounds like sucker growth off the roots, which by now have extended under your lawn. Tree or lawn, as Spritzhenry says.

Many thanks.
I think it must be sucker growth as there are about 20 of them (at present) in my lawn and they are about 2 - 4 inch patches of slightly hard growth, level with the grass. They are spreading about twice the distance of the canopy and progressing further as time goes by.
At present I just mow them as they grow. Can I dig them out, or am I just wasting my time?
Is my only option to cut the tree down, or will the roots continue to grow anyway?
Thanks
Richard

Unfortunately, even if you took the tree down, you'd find sucker growth still occurring, in fact, it might even be more noticeable. I'd keep mowing over them...

That's what we do with poplar tree roots and suckers.

Thanks to both of you for the advice, much appreciated.
Regards
Richard

You're welcome, Richard.