Firstly, just because over half the council has a disclosable interest doesn't necessarily mean a dispensation should be given. If you still have a quorum when those excluded from voting are discounted, there is no need for a dispensation. The guidance generally states that a dispensation should only be given if the business of the council cannot take place without a dispensation.
Ideally you should have a dispensation policy which broadly sets out the points I've covered in my first paragraph and also sets out how a dispensation can be granted. Also check your standing orders as these may identify the procedure to be followed. I believe there is no set procedure in the Localism Act but am happy to be corrected. In the absence of a policy your full council (excluding the individual seeking the dispensation) can vote on the granting of a dispensation so you'd need to take each request separately. Many councils have a set policy which delegates authority to the Clerk to grant a dispensation in accordance with the stated policy, i.e. when the request meets the circumstances allowed for in the policy statement.