They don't need to persuade them. They (or rather their borough council on their behalf) have the power under Section 39 of the Small Holdings and Allotments Act 1908 to compulsorily rent or buy the land. If they don't have the money to buy the site then they can rent it at an agricultural rent - something like 60p/pole - way cheap enough to recoup through allotment rents. The question to ask the council - the question many of us need to be asking our councils - is why, when they have a duty to provide allotments and the power to do it at no cost to the tax payer, are they sitting on their hands.