No. Henry VIII broke away from catholicism and took a load of the Church's money (from what I remember from history). The Queen is the head of C of E. It's essentially the same religion though I think.
In the Anglican Church Service - which is Church of England - we do acknowledge the Catholic Church so it's all part and parcel, but you are not considered to be Catholic.
I'd also like to be pedantic!
Catholic means "universal" and can be applied to any and all christian religions. I vaguely recall a line in a prayer (or similar) used in one of the protestant churches that refers to the holy catholic church.
The mainstream usage for catholic refers to Roman Catholic which is the church headed up by the pope. If you were christened Church of England, then you are not a Roman Catholic.
Half an hour's research on the internet could fill you in on the differences between CofE and RC, they're really quite small. Then you could go to either service!
if you really want to be a catholic, then convert. although i guess following catholicism counts as converting, there's an official way to do it (not sure what, having only converted from catholicism-by-default to atheism by sense)