I am sharing this situation as I believe it may not be a very common one so I hope some of you find it useful or at least interesting.
My wife and I were in the process of applying for ILR (sent a post application on 01/07/2013). During the application process, my son was born on the 1st November, which was exactly the same day in which the Home Office approved our ILR (as per the date included in the letter notifying us of this). I searched for information through the whole Internet to confirm whether my son was born British, but was unable to find some very specific information like this. When I went to register my son in the Register Office I enquired this. The Register Officer was unable to confirm this, but she call the Home Office in that moment. The Home Office confirmed it
In summary, although it is not mentioned anywhere and based on my case, If a child is born in exactly the same day as an ILR status is granted, then this child is British. This will save you around £600 and doing all the paperwork that needs to be done if the child had to apply for citizenship.
Jose