Sorry - I was a little bit confused as to the nationality of the OPs mother.
I thought she was australian.
Re 'free' insurance: if she is australian - full medical cover, in a public hospital, would be provied in the UK.
If a NZ citizen - the same will apply from my initial reading - see link here:
http://www.moh.govt.nz/moh.nsf/index...#newzealanders
A NZ citizen also has free health care in Australia.
So that covers cases of emergency / immediate care (the reciprocal arrangements don't cover elective surgery etc etc)
To Henkybaby - our travel insurance works slightly differently in Australia and NZ - generally cover for the elderly finishes at something like 70 or 80 - after that you can pay double premiums - but there is generally an upper age limit of about 85 or 90 (all ages are depending on your policy). It's a bit unfair - my parents are just fine but their policies are extremely expensive. Private health cover in Oz at least, not sure about NZ, doesn't cover us overseas. You can buy a separate policy from our private health insurer - but these are subject to age limits and hefty premiums.
Australia's free insurance arrangements are very comprehensive - covers about 10 or so countries around the world. Looks like NZ is much more limited.
And finally in response to the poster re visa for Oz - as a NZ citizen no visa is required (unless of course she has committed a crime with more than 12 months imprisonment!!)