GMorrison:
There's a lot of options and opinions floating around about dating the BoB.
The RAF website says it began in "early July" (http://www.raf.mod.uk/history/thebattleofbritain.cfm)
History Channel says it started on 10 July, 1940 (http://www.history.com/this-day-in-history/the-battle-of-britain-begins). Britannica seems to agree (http://www.britannica.com/EBchecked/topic/79855/Battle-of-Britain). So does Battle of Britain blog, with the Kanalkampf (http://battleofbritainblog.com/).
The BBC says it started in the "middle" of July (http://www.bbc.co.uk/history/battle_of_britain)
And the Battle of Britain website (http://www.battleofbritain1940.net/0021.html) further adds this compilation of opinion:
Richard Townshend Bickers in Battle Diary - Battle of Britain claims that there were four phases.
Phase 1: Aug 8 - Aug 18. Phase 2: Aug 19 - Sept 5. Phase 3: Sept 6 - Oct 5. Phase 4: Oct 6 - 31.
Norman Franks in Fighter Command Losses also claims there were four phases but with different dates.
Phase 1: July 10 - Aug 7. Phase 2: Aug 8 - Sept 6. Phase 3: Sept 7 - 30. Phase 4: Oct 1 - Oct 31.
Derek Wood & Derek Dempster in the Narrow Margin claim that there were five phases.
Phase 1: July 10-Aug 7. Phase 2: Aug 8-23. Phase 3: Aug 24-Sept 6. Phase 4: Sept 7-30. Phase 5: Oct 1-31.
Len Deighton in Fighter-The True Story of The Battle of Britain claims four phases.
Phase 1: July 10 - Aug 11. Phase 2: Aug 12 - 23. Phase 3: Aug 24 - Sept 6. Phase 4: Sept 7 - 15.
John Ray, Battle of Britain - New Perspectives uses only three phases in his book.
Phase 1: July 10 - Aug 18. Phase 2: Aug 19 - Sept 7. Phase 3. Sept 7 - Oct 16.
The owner of the above site leans toward starting the BoB as soon as the Battle of France was finished--referencing Churchill's famous remark. That would put the beginning of the battle into June.
Based on all this, it seems to me that--although the GB might not start till August--it would be OK to build something that may have been flying around in England and over the Channel convoys as early as June, 1940 and continuing through the summer.
My opinion only; I defer to our GB leader of course for the definitive answer about what does and doesn't fit into the GB.
And we can note from above that most British opinion is that the battle ended in September or October, not when Hitler decided to postpone SeaLion indefinitely.
Lots of room for historical opinion, one of the things that keeps history interesting, I think.