To get a good protest, you need an organisation or organisations to do the legwork. With something like nuclear weapons there's a clear thing to protest against and, at least in the UK, a decent-sized organisation with plenty of local representation to act as a catalyst. Likewise with the fox-hunting debate, there are organisations either side to rally their people to attend large-scale demonstrations.
With Brexit, it's not clear who should be doing the organising at this stage. Both major political parties are now pro-Brexit (still don't know how that happened, especially with Labour where the membership and, more importantly supporters, were strongly in favour or Remaining - but nevermind) and in any case if a political party organises it, people from other parties will not attend.
An organisation like the TUC could do some organisation but it's not clear what the possible impact on jobs and public services is likely to be. AFAIK there isn't an adequately funded pro-Remain organisation to organise and lead any demonstration.
I can see how there would be demonstrations in Scotland, the views of a country have (once again ?) been brushed aside by Westminster - which IMO does provide more of a point of focus.
