My god, you'll need a holiday to get over this one!

Day 1 - I think Heathrow to hotel, then Lloyds and then lunch is ambitious. You'll be tired (pills or pillows notwithstanding) and won't get to the hotel much before 11am.

Day 5. Harrods is rubbish. As much of what you are seeing is classic tourist London why not visit something slightly different. A walk through Notting Hill - nice area, interesting boutiques etc. Explore somewhere like Marylebone which is central, but a bit more real London. A picnic in Regents Park afterwards perhaps?