Can I start right away?  

To set up a sole trader business through allows you to start business the same day.  

To set up a partnership will be just as quick as long as you and your partner have an agreed partnership agreement that you can upload when you register. 

To set up a private limited company will take about 5 days while you register it on and draw up the rules governing the business, the Articles of Association (probably in collaboration with an accountant or solicitor). To set up a public limited company is much more complicated and costly and is probably not relevant at this point.