How exciting that you are thinking this way. If you have current British passports then you can just walk in. You can keep both passports. When I travel I always leave Australia on my Aussie one, and enter the UK on my British one. The airlines and customs staff are used to it.
I grew up in Australia but to British parents and have never really felt at home in Australia - I always knew there was something a bit different about me but could not put my finger on it. So much of our culture comes from Britain that when one goes there it really can feel like going home. I certainly intend to go back and live there one day. It feels much more like the world is happening there, whereas in Australia I feel the world is passing me by.
Re employment, it may be easier to line up a job once you are there but if you need job security tap your family network or try Gumtree/LinkedIn/whatever you like to use.
Good luck.