How much root do I need to dig up to stop unwanted ash trees growing back?

So, a couple of months back, the helpful folks on here advised that these trees are probably self-seeded ash, which I probably don't want to keep (well, I'd already decided I didn't think I wanted to keep them, but folks on here confirmed me in my thinking).



Having a lack of funds to pay anyone else to deal with this, and having an arguably foolhardy gungho attitude, I have this week started trying to get rid of these trees. Yesterday I managed to get down to one of the sizeable roots of the trees:




Today, with a combination of fork, saw, pickaxe and mattock, I managed to cut right through that root a short way along from the tree stumps and start pulling it up, thereby discovering that two branches of the root both went quite a way out into the lawn:



In the photo above, the ends of both branches of roots are still thoroughly stuck in the ground. My inclination is to chop both branches of roots (using secateurs / saw), thereby allowing me to ditch all the section of root shown in the photo above - but is there any risk of anything re-growing from the bits of root left in the ground?

Additionally, on pulling up the root shown above, I came across another section of root, which - so far as I can tell - could be ash tree root but could be root of one of the adjacent shrubs I want to keep.



So, main question - if I manage to dig up and remove all the major branches of roots attached to the bottom of the tree stumps, will that get rid of the trees, or is there any risk of anything re-growing from smaller bits of root if I leave these in the ground?

(If anybody has any tricks for trying to get at the root growing right by the wall, that would also be very welcome. Am guessing I'm just going to have to hack away at it any way I can.)

Thanks in advance.

 

as long as you get the main roots out it should be fine

 

Dig out as much as you can. Cut off etc and give what's left a good coating of SBK. Leave the ground open for a while.

 

Like Mike says, hit it with weedkiller.

Early on, I was told to use weedkiller mixed with paraffin. Cut the tree down, cut a deep X (or other grooves) in the stump, and pour the stuff on. Never had anything grow back after that.

 

They used to suggest mixing SBK with diesel.
I don't think they do any more.
Pretty nasty way of going about it environmentally.
Not 100% sure but I don't think ash suckers, so if you get the main stem and immediate roots the rest will just rot.