I'd suggest Bovington, Duxford, Churchill War Rooms and Dover Castle.
Plenty of naval history in Portsmouth, as has been said, and there's the D-day museum over in Gosport.
Bovington - the worlds largest collection of tanks, and the only place you can see many of them.
Duxford - a ww1/ww2 airfield, Monty's tank and command caravan, loads of vehicles and probably the best collection of military aircraft in the world. Also the home of the american air museum. More than can be done in 1 day. If you stop over there's also Madingley cemetery to pay respects, and the Shuttleworth collection (vintage vehicles and the early days of flight)
Churchill war rooms - Churchills command bunker. Tie it in with the toursity bits in London, as it's right in the heart near Downing street, Buckingham Palace, Big Ben etc. Also try for HMS Belfast - a ww2 battleship (Town class cruiser, next to tower bridge), The Tower of London, etc.
Dover Castle - a medievel castle, and also home to the maritime command bunkers where the Dunkirk evacuation was planned/commanded and an underground hospital.
Of the lot, the one I'd not miss out on would be the Churchill war rooms - seeing the map on which almost the whole of the ww2 allied effort was run from, covered in millions of tiny pin holes in patterns for the fronts and shipping/supply columns, is utterly fascinating. Also Churchill's toilet (actually the hotline to the US). It's not a full day though, so you can plan other things.