I have 2 buggies (and a sling but tge cold has got into my back grrr hence this thread). One is a standard travel system one (Mothercare)- heavy but super comfy. The other is a Silver Cross Pop (Maclaren style). I bought the pop so I could use it on trains/buses.
I'm going into central London tomorrow and was going to use the sling/carry the folded stroller but my back is killing me.
I can get the overground step free from a local station to Paddington.
If I can then use a black cab to my destination I understand from old threads this was ok a few years back - is it still ok now? They used to just strap them in like wheelchairs from what I understand?
I am very pfb/anxious about taking dd up an escalator or steps without someone "spotting" the bottom as I hold the top of the stroller (she's 4 months, it has good straps, reclines and is light enough). 
If black cabs take buggies that would be so amazing.