Byelaws do not cease to have validity over time, unless the actual byelaw includes a termination date, which would be very unusual. So if you have an existing byelaw made in accordance with the legal requirements at that time, it is still enforceable. I agree with everything Prestonfan says about PSPO's as a way of addressing dog exclusion.
If you want to create new byelaws or amend the existing ones, the process became simpler in 2016 with the delegation of powers to local councils through The Byelaws (Alternative Procedure) (England) Regulations 2016. Parish, Town or District councils undertake all of the preliminary work, drafting (often using a model wording) public consultation, impact assessment etc. The new process includes consent from the Secretary of State, but the turnaround time for this is limited to 30 days. There is detailed information about the process and timelines on Gov.uk.