large back garden full of baby trees from giant trees nearby

Do you want rid of the seedlings? They should not be that difficult to just lift out, especially after heavy rain or a good watering.

It depends how big the baby trees are, Kildermorie. The roots are likely to be at least as large as the growth you can see, Mouseybrown. Pulling the seedlings or saplings out is the quickest if they're small enough, otherwise you'll need to dig them out if you can. I find saplings of any size are very resistant to weedkillers like Roundup. You can think they've been killed off, but they come back, all bonny & bouncy the next year.

As a last resort for trees that are too big to get out, you could use brushwood killer - carefully - but don't get it on anything else. SBK is a brand that's often recommended on here, but I haven't used it personally, preferring elbow grease, so far!

Get them level first and any other trash needing to be moved then get mowing. Lopper, chopper, pruning saw. Hard graft. The mown area will settle out to grass if regularly done. Sheltered accomodation next door had young cherry saplings in one grassed area. Now it is lawn again after new contractors came in and cut regularly. Why do more if in rented.....

You said they were 'giant trees'! I would be cautious here as just pulling them out could make it worse? If they are trees from the Populus family such as willow/poplar (up to 35 species) the roots spread under ground up to 150 yards and go very deep. But as you are in rented I would identify the trees and take photos of them in the garden and send the info to the landlord as they may well care enough to do something.