I don't know much about gardening but could this be Moringa? We have them in the Maldives so I thought the leaves look a bit familiar.

sooo ... are you also in the maldives???

Alas, I don't think Moringa - right colour and leaf shape but none of the spikes. I realise it would have been helpful to say we're in the south if England!

Do you have any black locust (Robinia pseudoacacia) trees nearby? They spread by suckers.

I second the Locust possibility... Especially in your part of the world. Are there any nearby? They're pretty distinct with chains of fragrant white flowers and pea pod like seeds. Very common and desirable trees in Europe. Do note that they need quite a bit of space.

Oh gosh, I just dug down... They all appear to be connected to thicker roots. Is this likely to be the culprit(see images)? Thank you for your help so far!

I've never seen the tree flower, but those bunches of what I thought were leaves appear to be seed pods....

The seed pods and tree aren't Robinia. I don't know what the large tree is.

I've just wandered around the other side of our fence as there's a large row of trees/shrubs screening the edge of our housing estate. But can't see anything like that Robinia! It's beautiful by the way, but I don't want a jungle of it in the middle of the lawn! Looking up 'suckers' on the Internet I'd say that's what they were.... But I can't see where those roots are coming from! We had a huge tree in the garden which my partner chopped right back (horrible spiky thing, I was worried these were revenge saplings!), but the leaves were nothing like these....

Those seed pods belong to the Ash family (Fraxinus) ... So,the large tree is Fraxinus excelsior -- European or Common Ash.

I still think your sapling is a Locust, though (could be Honey or Black). The leaves, thorns... It's tough, sometimes, to ID such young trees. There are even some "weeds" that are dead wringers for certain trees.

I think you're right... Having looked up the Robinia 'suckers' specifically they look pretty much identical. Why would they suddenly pop up on the bare patch? Do they 'know' there's no competition from other plants? Wish I could see the blooming 'mother' tree!

Robinias are known for producing root suckers........and robinias get to be large trees so their root systems can spread out quite a distance. The mother tree, from whose root system these suckers are emerging, should be somewhere within about a 100 yard radius.

Besides the root suckers, don't forget they have a very high seed germination rate ;) Here in the US -- where the Locust trees originated -- I've seen critters eating the seed pods (mainly deer) which could sprout new trees far from the parent. Storms can also blow the pods off the trees =) The parent should be nearby, but may not be ;)