HMRC guidelines have changed for registering your business with them. Previously you had three months to register before being subject to a penalty for not registering within this time but now HMRC ask you to register as soon as possible or by 5 October in your business's second tax year. You will not receive a penalty as long as you submit your tax return and pay any tax due by the due date.
So if you set up your business between March 2015 and April 2016 you will need to register your business with them by 5 October 2016. Your tax return will be due by 31 January 2017 so if you leave it too close to 5 October to register you will not have the option to file a paper tax return which must be done by 31 October. If you submit after 31 October you will be able to do this by completing a tax return online. You must register for online services to be able to do this and you should allow at least 10 days to receive the activation code from HMRC which will allow you to access your account.