I called them up directly to get the facts straight and these are the steps:
1. Call the Jobcentre Plus application line
- Telephone: 0845 600 0643
- Open Monday to Friday, 8am to 6pm
2. Give them the following information
- Date of Birth
- Full UK Address
- Passport details
- VISA details - visa number, type of visa, where it was issued and expiry date
3. They will send you a form to fill out which you need to return with a copy of your passport
4. Do the happy dance because... that's it!
It'll take around 3 weeks to get your NI number but you can start work without one. Just note, there is you might have to go in for interview if your VISA has been reissued in the UK or if you've come over on a British or EU Passport.
If you have any questions or would like to know how it works for non Aussie / Kiwis, call the Jobcentre Plus directly on 0845 600 0643 and they'll be able to help you out.