Para 25 is a clear and concise outline of the restrictions on individual councillors and they're there for a reason, but beyond those vital limitations, you're free to talk to anybody you want, particularly if it's helpful in gathering information to assist the council in its decision-making.
Having said that, you might wish to consider something less confrontational than a fight and simply ask the Clerk to quote the legislation that prevents you from contacting your district council. Save the boxing gloves for round two!
My councils use a portfolio system under which each councillor volunteers to take responsibility for a small part of our work, so the highways councillor monitors and reports faults, as do the street lighting councillor, the grounds maintenance councillor etc etc. As Clerk, I wait for them to report their actions to the next meeting. They can't incur expenditure on behalf of the council, but they are free to instruct the relevant parties where something needs to be done.