From the photo your garden is full of potential, and I love the fact that you have different levels. Unless your children have mobility problems, I don't think you need to worry about the different levels - they have the flat concrete to push wheeled toys about on, set out toy farms, race tracks and all sorts of other toys, and a grassy area for a different sort of play. I can see they've got swings up there under the trees. Believe it or not they don't stay toddlers for long, and learning to cope with slopes, steps and uneven ground will add to their mobility. I think your garden looks idyllic for a family.
If you tried to level it off, by moving soil from the higher level to cover the slab, you'd encounter the roots of those big trees you have on your boundary. Uncovering them may make them unstable. As it is those trees provide a lovely windbreak and I'm sure you must have lots of birds and a hedgehog or two living there. All wonderful ways of introducing your children to Nature as they grow up.
Also, changing the levels of your garden to that degree is likely to affect the soil structure and water table causing drainage problems which could also damage the trees either by drying them out when removing soil, or waterlogging by raising the lower level, or both - I would have thought it a good idea to get advice from a landscape engineer before starting on a project like that.
From the photos I can't see anywhere that I'd be worried about small children falling down the bank - they could only do that if they were in the flower beds around the concrete slab, and while they're that little they're not going to be playing out there unsupervised are they, and if they go into the flower beds you're going to move them and tell them gently not to and that's how they'll learn not to walk on flower beds
When they're bigger they'll know not to go in the flower beds so won't be in danger of falling down the slope.
The advantages of having a large area of concrete which will dry quickly after rain so the children can play outside are immense - when they've grown too big to 'play in the garden' there are lots of possibilities if you want to change the layout of the whole garden - you could terrace the whole area maybe?
But you'd have to break up and remove the concrete and the hardcore etc which presumably is underneath it. Please don't try to put soil on top of concrete - all that effort will be wasted as the area won't drain properly and I don't think it would be stable.
If you're really worried about them falling and bumping their heads on the concrete while they're very little, you could look into buying some of those rubber play mats, or even have the area covered with a permanent safe surface http://www.softsurfaces.co.uk/ but I've no idea how much that would cost and to be honest I think that would be a little extreme in a normal family garden - but of course necessary if a child had a condition like an abnormally fragile skull, brittle bones, or drop seizures or something which increased the risk.
As I said I think your garden is lovely and very similar to the one we had when my children were small, except our flat area was at the top and there were several different levels going down the hill to a stream at the bottom - we fenced them out of that bit until they were around 9 or 10 and had showed they could be trusted - then Daddy showed them how to dam the stream and flood the neighbour's garden, but that's another story