would having a head teachers appeal (head has said we have full support ) hinder our chances at appeal to our chosen school is unsuccessful?
It depends whether the admission authority will seek to argue at an appeal that there's already been a 'fair, consistent & objective' review. In Medway and Bucks they do, which is a serious problem. In Kent (to their credit) they don't.
I don't know about Bexley - you'll need to enquire. Try asking the grammar schools.
The only thing I could find on the council's website is:
Please note that selective decisions will only be
changed by the Review Panel in exceptional circumstances
Note the word "exceptional".
However, you do need to investigate the success rate for appeals at the school(s) you're interested in - it's not impossible that favourable decisions via an appeal are also "exceptional".