I'm pretty sure I will do that. I've been to most of the parks already - on the first day by bike and later on foot, although I will definitely go back to some of them again.
I did most of the touristy stuff you mentioned and some others, plus spent Friday and Saturday nights at various museums. It was the Museum Night weekend and there were so many interesting tours and events in many of the museums. I walked around a lot, browsed the pubs , did some shopping (fell in love with Desigual on Regent Street . I've ordered a few things from Desigual online, but this shop was like heaven on Earth .). The last day before catching the train back I had thought to quickly hop in the Camden market, but ended up spending most of the day there.
I have an idea of the city now and can prepare for the next visit a bit better, I hope. Although we might go there by car in summer, I doubt I will be able to drive there . I've got used to driving on the left by now, but traffic in some parts of the city is just too crazy for me, I'm afraid.
I didn't know you lived in London! I wouldn't mind living there for some time, but I doubt I would want to make it my home.