@Stephan I can sense your frustration after a year of inadequate responses. For bureaucracies, the important thing is following "procedure", so given that all the arguments are on your side, this is what I would do.
Download the Complaints procedure from the council website. Put in a formal complaint (making sure you include the fact that you've been trying to get a satisfactory response for a year by less formal means) explaining that the gate is not useable by any non-standard bike, that the notice they put up is not an adequate response and why, that the gate does not follow recommended design practice, that the mere presence of any gate doesn't follow recommended practice, and you want it removed. Include the other valid points you have raised.
They are obliged to reply to you within a specified time. You may not win first time and you might have to continue with the complaints procedure by appealing against their first response. When you have gone through the procedure, and if you still haven't got a satisfactory response, then you can refer it to the ombudsman.
Good luck, ih.