Firstly - what an amazing holiday - my kind of trip, I would love to know what is on the schedule in London and you are going to the festival/tattoo/fringe in Edinburgh right?
Secondly, I think you need both a pair of closed in shoes and a pair in sandals. I know that England has a reputation for rubbish weather, but it can get hot and sticky and sandals fit the bill in that type of weather. Plus, being able to change your shoes does wonders for sore feet! In fact for 14 days, I would take at least 3 pairs of shoes minimum - so one nicer closed to, one pair of sandals and a pair of converse or similar.
For closed toe shoes, how about a pair of Clarks like these - http://www.clarks.co.uk/find/b.....s-20339633 . I bought these with a MOTG friend and she loves them!
I also recently, at the suggestion of someone on the forum (I'm sorry I can't remember who) got a couple of pairs of these inner soles - http://prettypinktoes.co.uk/insoles.aspx . They feel amazing and have kept my feet cool and comfy...
Lastly, anytime for a cup of tea?