Ruddy - I'd try Premier Travel Inn, as they have one just near the Globe, and I've always thought that if I had to stay at a hotel in London it looked good. The problem with living in London is that you never need to use hotels here, so don't have a list of recommendations!
As a general rule, Premier Travel Inn is great if you have babies, as their cots are always perfectly made up, and there is always a child friendly restaurant attached. We use them a lot on the journey to Scotland to break the journey. Their rooms are always a good standard, and clean.
For getting around, I'd recommend the sling, as a lot of the tube system is inaccessible on wheels, and this will make buses easier too. Do you have Oyster cards? They make traveling a lot cheaper in London, and your guests can hand theirs back when they leave to get back cash and deposit - you might as well keep yours for your next trip.
Anyway, back to me! Ugh, I do want some form of a routine, just so I know what to expect! The night before, E didn't wake till 5 am, this night, the third waking was just after 5! She's now asleep in my arms, as I want DH to get half an hour of uninterrupted sleep before the alarm goes off, as E has been shuffling most of the night!
And we also love vests here! DS is always got a vest style body suit on even at 2, as he likes to be carried, and his day vest stops everything from sliding up. I'll be sad to see them go when potty training commences, but don't think that will be for a while yet!
On the reflux babies, my mum thinks I had it, but as I was piling on the pounds, it didn't cause problems, but she really wishes she'd been able to get infant gaviscin all those years ago, just to make raising me less stressful - she remembers me as a difficult baby!