I am very late to this thread but I agree that what @Wildlifeinthedark says is correct.
The OP, @Jeelypieces20storeys owns the "dominant" property that has rights over the "servient" neighbour's land.
In this situation, the neighbours are not required to maintain the right of way at all but the OP is certainly allowed to maintain the path to a suitable standard - and, yes, this does include weeding and replacing broken slabs.
I'm sorry to say this to all the people, like those below, who think that the OP isn't allowed to replace broken slabs in other people's gardens in this situation, but you are wrong. It has been the law in England & Wales for the last 242 years (since 1781) that the dominant property owner (ie the OP):-
"...is entitled to maintain and repair the way and, if he wants the way to be kept in repair, must himself bear the cost"
Taylor v Whitehead (1781) 2 Doug KB. Cited in Carter v Cole [2006] EWCA Civ 398
To the following contributors, I'm sorry but you really are wrong on this point:-
@akkakk
@maybebalancing
@Aprilx
@Boomboom22
@Tinkerbyebye
@ImABox
@applesandmares
@calmcoco
@DiscoBeat
@Hufflepods
@YetMoreNewBeginnings
@OhLookIveChangedMyNameAgain
@IfYouDontAsk
Also, to those who said that her sisters couldn't use the path, anyone who has a lawful reason to access the communal garden from the OP's property - basically anyone other than a burglar - can freely use the path.
ps There was also another case that said that rights of way can actually be improved if they do not meet the required standard. So, for example, if the right of way includes vehicles but it is just an earth track, then the owner of the dominant property can improve the right of way:-
"If you grant to me over a field a right of carriage-way to my house, I may enter upon your field and make over it a carriage-way sufficient to support the ordinary traffic of a carriage-way, otherwise the grant is of no use to me, because my carriage would sink up to the naves of the wheels in a week or two of wet weather."
Newcomen v Coulson (1877) 5 ChD 133 cited in Nationwide Building Society v James Beauchamp (A Firm) [2001] EWCA Civ 275