Haven't visited this website in many years. Moved from London to Chandler's Ford last year and just happened to login again to see if any local astro meetups down this way. Coincidence that the first thread I stumble upon is yours.
During my Sunday afternoon internetting I've found these two clubs: https://hantsastro.org.uk/ These guys seem active and are over Pompey way.
http://www.solentastro.org/ These guys are closer to Southampton, but a fair bit of the info on the website is out of date so wonder how active they are.
I'd imagine there are some decent dark sky spots in the Forest. Anyone more familiar with the area have any suggestions?