Can I make a request for someone else?

Yes. First register yourself as a user at the practice where the person who needs help is registered. Once you are registered, there is an option to select 'I am asking as a Parent or Carer.' 

Then, choose 'Someone else' to add a new person under your care:

Finally, fill in the details of the person you wish to submit requests on behalf of and then select 'Register':

You can also view the list of people under your care, add new patients under your care, and initiate a request on behalf of them via the 'Patients I care for' option in the main menu

Note: If you are already a patient using askmyGP at your own practice and you wish to become a proxy for a patient registered at a different practice, you will need to create a separate proxy account at their registered practice with a different email address - duplicate emails are not supported.