I believe that said av. Londoner would only think of non-water birds.
Well, I live down in the middle of Sussex and commute each day so cannot claim to be an average Londoner and I don’t think I know an *average Londoner, but those Londoners I have met are reasonably aware of the wild life to be found in their city. There are also seagulls, crows, rooks and magpies (and even ravens!) to be seen in London which are rather larger than the smaller landbirds you mentioned. From my office window I can sometimes see kestrels and hawks, it is hard to tell, against the brightness of the sky, what kind of hawk; they just circle lazily up there. The kestrel has always been common of course but, following a programme of reintroduction, several other birds of prey are quite often seen in southern England now. Currently, hunting in our home area, we have a sparrow hawk that upsets the local children who sometimes see it make a kill in their gardens!
(Mind you, when a swan does decide to fly, it is an awe-inspiring sight!)
This may be a self-YART, but what the heck.
One evening I saw a swan flying over London. I am not good at estimating heights but I would guess it was flying at perhaps four or five hundred feet. The sun was reflecting from its feathers so that the bird had a golden sheen as it forged its way steadily northward. To be at that height it seemed that it must be going for some distance. The picture of that solitary swan has stayed in my mind ever since together with questions as to what pressures were driving it on. It was certainly both awe-inspiring and affecting.
