Hmmm we had a similar problem a few years ago, as it was a council fence, then they really should have contacted you about it and the HA first. Nevertheless, its too late for that now, what I would suggest is to ask the HA for them to put up a fence as a neighbourhood dispute will ensue.
There is another alternative, if you and your neighbour cannot resolve this amicably, then maybe self referring yourself to a mediation service will help resolve issues.
Something so small like a trellis CAN turn into something big, so nip it in the bud now.

I am sorry to hear that your neighbours are being very silly about this but dont worry yourself about it.