Roots in flower beds

Hi all.
I've been weeding my neglected flower beds... I've used a fork and Dutch Hoe to get rid of as much as possible. Pictures of before and after are below.

I've posted a close-up of the soil after weeding... It's full of lots of little roots. Do I need to take these out too, or will they die off on their own?

Thanks in advance.

 

Hi,

Very hard to say what plant those roots belong to ?

For now I would just leave them, they will probably die off now they have been exposed.
From your first pic you clearly do not have a rampant weed problem.

I suspect they could be part of the trees you want to keep.

Generally you do not want to hoe more that an inch or two below the surface to avoid such root damage.
How deep are you going with the hoe and fork ?

You could carefully spot treat the 'weeds' with a glyphosate weed killer instead.

Seems there are some plants comming in from under the gravel board, are there a lot of plants trying to get in from behind the fence ?

 

Thank you for the reply! The concrete blocks at the back are coming out tomorrow, so there will be no plants coming in from there. They're on our side of the fence.

I've been hoeing the surface soil about 2-3 inches. With the fork I have been attacking the big clumps. Sometimes up to 5-6 inches deep. The weeds are growing from little bright white bulbs.

I would buy weed killer, but I guess it's not classed as an essential!

The tree roots are right near the surface, so I am being extremely careful not to damage them and work around them... I will be making the beds deeper over the coming months. The bricks will be replaced with sleepers and more soil added in