If we are claiming Gift Aid on membership fees, do the same rules about Income tax limits apply to the members as apply to individuals making a donation?

Yes, any individual whose payments (membership subscriptions or donations) have Gift Aid claimed on them must not pay less Income Tax and/or Capital Gains Tax than the amount of Gift Aid claimed on all their payments (not just ones made to your charity) in that tax year. Otherwise, they will be liable to, and responsible for, repaying any difference to HMRC.