The two threads you need to consult are:

https://www.flyertalk.com/forum/brit...need-know.html
and
https://www.flyertalk.com/forum/brit...261-uk261.html

both of which are in the BA Forum Dashboard if you need to refer to them in the future, and which is where I found them for the links above.

In essence you will get your reasonable hotel, meals, wifi and travel expenses refunded. You may be entitled to delay compensation too, but it depends on the cause of the cancellation, which presumably you asked about yesterday. If you paid for a ticket for your child then they also get the same compensation payment.