A closer marco photo shot of the leaves would make it clearer, but the
"thin
white tails" suggest its bindweed

I agree but from the pictures it looks like ground elder.

Either way if it is coming across from next door you are unlikely to be able
to eradicate it as it will always creep back. I'd just spray with
glycophospate and/or pull up any bits you see on as regular basis as
possible (at least once a week). this should at least weaken it

--
Hayley
(gardening on well drained, alkaline clay in Somerset)