Mid June would be a good time. As to things to include - I'll limit myself to 7 suggestions:
Stratford on Avon
Blenheim Palace (Churchill birthplace + he is buried in the village churchyard IIRC)
Haynes Motor Museum at Sparkford (others can comment on the food there!)
Fleet Air Arm Museum - Yeovilton
Stonehenge
National Motor Museum - Beaulieu
RAF Museum at either Cosford (nr Wolverhampton) or Hendon (London)
You can easily spend 2-3 days in London. You might consider taking in a show whilst there.
