It is more likely that the Airline will deny boarding in the UK if you do not have a visa or proof of onward or return travel. Heathrow in particular is getting quite tough on this.
I have always done it a minimum of 8 days before, just so I don't have to worry about exactly this question :). However yes, the 12th would be correct.
I am not giving advice, I am simply stating a fact. I cleared the overstay's at the airport each time and i have never had any trouble about this since.