Well, it can also be translated as "When he had conquered...."  or "After he had conquered...." so then it's (I guess) an adverbial modifying clause  (certainly a dependent clause).

On Friday, February 14, 2014 3:43 AM, Jyri Lehtinen <[log in to unmask]> wrote:
2014-02-13 0:12 GMT+02:00 Jeffrey Daniel Rollin-Jones <[log in to unmask]

> Isn't "having conquered Gaul" in "Having conquered Gaul, he set about
> invading Britain" and independent clause? Or is it somehow "part of"
> "he...Britain"?

It's a dependent clause (does it sound grammatical when uttered on its
own?) and very much a part of the following independent clause centred
around the finite verb "set". It's an adverbial complement to the main
clause transmitting information related to the passage of time (here the
order of actions) and not too different from non-clausal adverbials doing
the same job, such as "in the next morning" in "In the next morning, he set

about invading Britain."