I had a similar experience recently on the other side of the river, though less extreme I think. Between London Bridge and Greenwich there are a few stretches that are ostensibly "public" but not that easy to access. Some are behind gates that are in fact unlocked, so you can just walk through, if you try, but they don't look very welcoming or accessible so I think a lot of people probably don't even bother. Other times the gates are in fact locked for non-residents and you can access the river by some other more roundabout way.
Bit of an aside, but although the area around Greenwich is lovely, I've always preferred walking the Thames Path out west, eg Putney to Richmond. Very peaceful and green, and IIRC all pretty accessible (apart from a stretch of the path near Barnes that is completely underwater when the tide is high).
I think the south side is the "official" Thames path, but I did think through London the north side was just as doable. I've walked the entire south side but not tried the north yet.
I do recall several difficult bits in the area you describe. One part seemed to have some new "food market" development, which was completely closed when we tried to go through. It got weirder the further we got and we questioned whether we'd gone wrong somehow. Eventually the path just stopped forcing us to double back and make for the road which added a mile or two to the walk.
We haven't had any such problems along to the west, all the way to Maidenhead so far.