Weed or flower?
Earlier in the year I cleared the ground around my Bramley Apple tree of a lot of ground elder. Since the disturbance to the ground ( deep forking and uprooting of the offending elder) this low growing plant colony has appeared.

I'm not sure whether to pull up, dig up or dig in. I don't know whether they are something that is supposed to be there (a lot of things were planted by by wife whom I lost two years ago) or is it a weed that will keep coming back?
Once the ground is clear again I want to replant some bluebell bulbs I salvaged during the removal of the elder roots. Should they go in soon?
The area has needed some attention for a few years and has been home to the ubiqitous grape hyacinth as well as the ground elder.
I would like to do more with this patch of ground so I was wondering what else to plant under the apple tree to help act as a less invasive ground cover?
Posts
Hi Birdie. Looks like chickweed.
Make sure you've got rid of the ground elder before you start another ground cover
In the sticks near Peterborough
There's common chickweed, Stellaria media, and one of the bittercresses there. Both annual weeds, pull them out before they go to seed, which they can do all the year round. You could just hoe them off as they won't regrow from the roots.
I missed the bittercress
In the sticks near Peterborough
yes chickweed - one of my favourite weeds - you can roll it up like a carpet - quick and easy!
it's a sign of fertile soil - lucky you.
Chickweed is good in salads and makes a lovely sandwich.
And as it's name suggests, used to be chopped up and fed to young poultry
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
I used to know someone who bred budgies and she fed it to them too
I live in west central Scotland - not where that photo is...
Yes, we fed it to our budgie, and he also enjoyed the seed spikes of plantains and a bit of groundsel when it had gone to seed.
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
Thankyou everyone for ypur advice and information.
Hm chickweed in salads...
I rather like that idea.
And bittercress...
Trouble is I'm not sure which is which.
Are they both edible or might I poison myself if i start eating my garden clear of weeds? 
Can anyone advise on a more suitable, less invasive ground cover for the area please? I need to start making the plot a lot more manageable for the future - ground elder and grape hyacinth permitting, of course.
What size area do you wish to cover?
Not a lot - I suppose about 4 - 6 sq metres around the tree. I'm happy to plant anything attractive that will suppress weeds and be easy to maintain.
As I would hope to still be able to get close up to the tree for pruning and maintenance I thought lowish ground cover plants would still enable be to get a step ladder in each year. Any ideas, anyone?