My mum is wanting to take my son from leeds airport to southampton, we've established that he doesnt need a

I ume from your question that they are travelling by public roads or transport, if that's the case your Mum doesn't need a letter from you, legally, however why not give her a letter of authorisation just in case she's stopped for whatever reason. It would save a lot of distress for you all if any authority had a doubt as to her right to be in charge of your son. If she's collecting your son from a flight at Leeds airport she will definitely need a written authorisation from you. I suggest attaching a copy of your pport/driving licence to the letter.