I would advance cautiously! Have you got permission as someone may well pop up if you do something such as the Terrace owners might think you are trying to take it? Contact the council or Land Registry to see who owns it and if you can get it cleared that way? Be open about your intentions or it could all back fire on you? Are there any shrubs/trees that could be saved or is it all rough?

You could just wait for winter and then clear the debris and deal with the saplings by either pulling them up (when the soil is damp) or digging them out. Alternatively, go and buy some Path weedkiller, the kind you mix in water, usually in sachet form, mix it up and apply with a watering can. Do that next spring too, before the weeds start getting too large - should keep it clear for 3 to 6 months, depending which product you buy. That won't deal with the trees or any woody based plants though, those will need to be removed or cut down and poisoned with a brushwood killer, such as SBK. I am, though, duty bound to point out that, if the area is a public right of way, and not owned by you, you should actually have a qualification and official certificate before applying any weedkiller, and in particular something as heavy duty as SBK or any brushwood killer, or things like sodium chlorate (which I do not recommend, its been withdrawn now anyway)

Round Up!

Thanks for the advice. I will take it all into consideration. It's mainly the nettles, ivy and other weeds that I have an issue with as these keep coming through. The big ones can just be cut back every now and again.
We've already contacted the council and landregistry and it's fine on that front. The terrace on the opposite side is rental so don't think they'd mind but will check with them anyway.
Thank you!

It's always a good idea to talk to your neighbours about things like this and who knows, they might be willing to lend a hand (or pay towards any costs involved?)

Your so right Ian when one suggests an improvement others get inspired too!