We are going to London, Paris, and Nice for our honeymoon in mid-Sept as well. Be prepared to fork out A LOT of money and effort to research. I have done about 6-8 hours so far. I'm slacking too.
$2500 pp seems to be okay. Save money by going
www.airbnb.ca we have never done that before so it will be interesting.
So far we have spent about $4500 total.
Flight to London $1250 each. BnB in Paris (5 nights) $1400 total and in Nice (3 nights) $600. I still need to find hotel in London 4 nights ($1000) and airfare/train between cities ($750 each for 3 trips).
With food, shopping, and tours... It looks like we heading towards $8,000-$10,000 total for two weeks.