Appointments for diabetes in the UK can be difficult to get, if you have recently moved over from Australia.
The NHS has long waiting times and appointments can take 2-4 weeks to get. Register for a GP as soon as you are able, once you have a permanent address. However, you can always pay privately to see a specialist if this is required. You would have next to no waiting times and may just tie you over until you are registered with a GP which can take a few weeks. All you need to do is Google Private GPs in London and a whole list will come up.