I'm not Pakistani myself and not aware of the nuances of Pakistani law. Therefore, I would be the wrong person to advise you on this matter.
Automatic citizenship is just that, citizenship without applying, by the action of law. A child born in the UK to parents with ILR will be a British citizen in the eyes of British law, even though his parents may not apply for or even desire British citizenship for their child.
A rudimentary search on Google turned up an official looking website (
http://www.dgip.gov.uk) that gave an overview of Pakistani citizenship. I advised you based on that.
Having said that, as you had another citizenship at some point in time, registering from a BNO to a British citizen appears to be difficult. The requirement is that at no point in time did you have another citizenship nor did you lose a citizenship through (action or) inaction. You had (and from the language of the website, have) Pakistani citizenship, which extinguishes your right to registration.
Again, I am no expert on Pakistani nationality law and I am advising based on the text found online. I am sure others more knowledgeable than me may advise otherwise.
Mind you, nothing stops you from earning ILR through other routes. Only the registration route is extinguished.