1. It's advisable to get the GPA attested by the Indian Consulate or Notary in London. You have to go personally to get the work done.
2. Yes, you have to send it to your father in India, who has to get it adjudicated in the jurisdictional District Registrar's Office.
3. When once the adjudication is completed, your father can execute the Gift Deed in your mother's favour, on your behalf, in the jurisdictional Sub Registrar's Office.
4. Gift Deed attested by the consulate in U.K. and sent to your mother is not the correct route. Your decision of authorising father through GPA is the correct one.