Re: London Visa
In UK contrary to everyone's believe. Emergency treatment to anyone in the country regardless of status is free. having said that only include ambulance service, and your treatment and stay at emergency ward at any hospital. But if you have to get treatment longer, you will be charged as visitor. but as aussi national you may have reciprocal treatment arrangement that may exist between UK and Aussi government. GP will not register you as visitor, but will see you and prescribe if require for nominal fee of £10 per visit. but travel insurance is better option.
for the main reason, traveling with your mother, etc, I dont think it will be a problem.