I am not familiar with these benefits and laws so i would suggest a call to ACAS directly for further information.
personally i doubt you would be able to claim if the child was already living under your care for a period before the adoption, purely because i think, like with maternity pay, its to assist with the readjustment of a new family member rather than a financial assistance.
I think you will find that you are unable to do much more than maybe take paid holiday if you need time together.
As i say though, give ACAS a quick call just to check.