Kitty, if you are taking black cabs, it's probably most practical to bring a pram/stroller (whose wheels you will lock in the back of the cab, and which you will secure with a wheelchair "seatbelt") and a sling (for comforting baby). The stroller will help you carry any paraphernalia, but at the very least I reckon:
- blankets and pramsuit/snowsuit (it will be Feb)
- inflatable pillow (for feeding), which squashes flat in a change bag. If you are breastfeeding, a small bottle of water to prevent you getting dehydrated.
OR any bottles/formula, hot water, etc. you need.
- change mat, nappies, wipes
- muslins for sick/posseting
- 2 changes of clothes (poos can go right up the back if explosive)
- wet bag for dirty clothes
- dummies if you are using them
Babies can sleep in prams with flat-reclined seats, so no duplication with aforementioned pram required.
Hope that stripped-down list helps! I have drawn up a travel list, which I keep as a document on my computer desk top and refer to it when travelling.
Presents are sort of happening here, although I'm making a lot - rather slowly. DH took DS out yesterday, and I wasted a the present-preparing time by fannying about on MN, eating, doing a bit of shopping in town, and finishing DS's nocturnal-creatures duvet cover! (owls on one side, hedgehogs on the other, a pillow slip of white stars on a blue background). The nocturnal creatures will look after him while he's asleep - good thing, too, as he had another screaming nightmare last night - about my eating some "green bar" of his! It was a bit off-pissing that it wasn't anything more scary than that. 
cheeptrick, have you something to tell us? 