Hi and welcome to our little MS community,
According to the MS trust Tysabri has been approved for use on the NHS since 2007, it is often prescribed in the UK when someone's MS is highly active though and the UK guidelines on paper are more restricted, so not exactly the same flexibility as here in Oz.
Theoretically from what i can work out, you shouldn't have a problem continuing taking Tysabri once your back in England but for your peace of mind, it would probably be a good idea to contact the neurologist who will be taking over your care and and try to set it up before hand.
https://www.mstrust.org.uk/a-z/tysabri-natalizumab
https://www.england.nhs.uk/wp-content/uploads/2013/10/d04-p-b.pdf
Cheers...........JJ