Nannynickers - we bought a MacLaren Volo buggy specifically because it was so light - DD is now 3 & we still use it as it's quicker than her walking sometimes! She's no lightweight, but up until last summer I could still manage to carry her upstairs in the buggy, it's that light. (I even managed it last month once when she fell asleep - 4kg of buggy and 17kg of child!)
My tips:
Wear a jacket with an inside pocket if you have one to put your money/rail ticket in. Failing that, a lightweight crossover bag that goes at your front (bought one in Marks the other day - v dull nylon but v light & useful)
Put kid's stuff (nappies/drink etc) in a backpack - take the bare minimum. Leaves your arms free then to manage puschchair/child.
It's easy enough to use the escalators with a small buggy. If you really don't like that, the Volo has a strap so you can sling it on your back and hold child (though you may get muddy wheelmarks on the back of your legs)
A lot of buses have buggy room so you don't have to fold it - follow where you're going on the A-Z if you're not familiar with the route.
I buy lunch out even if just a sandwich as it's one less thing to carry.
Look at the London Underground website which has a disabled access tube map - that shows stations with step-free access to the street, although it's actually better than the map suggests for buggy users as some stations may not be step-free but have only a few steps - it's trial and error really but in general the Jubilee line is good as it's more recent.
Hope this helps - sorry if rambling - must get on and do bathtime!