We generally don't spend more than 3 hours in a museum or other indoor attraction because by that time I'm overstimulated by seeing so many things, and being around people in an enclosed space.
We have never taken a tour at Westminster Abbey or St. Paul's Cathedral but have toured on our own and attended evensong services at both. At St. Paul's we have twice climbed to the top of the dome, and enjoyed talking to each other across the Whispering Gallery. Also enjoyed walking the cloisters at Westminster Abbey after evensong, though last year they were closed for refurbishing so were only allowed to walk as far as the toilets!
The ancient Egypt tour that Stacie mentioned might be worth it if you want to see the mummies, etc. We were visiting the Sutton Hoo exhibit, the Lewis chessmen, and the astrolabes last June, and found those displays fairly uncrowded. I wanted to see the cat mummies on the way out and almost had a panic attack. You could barely move in those rooms. On the other hand, we were there in late September one year and had no real crowds anywhere in the museum.
Went back to the Tower of London last summer, almost 20 years since the last time we went with our sons. We took a White Tower tour back then, but just walked around on our own this time. We particularly liked walking through the wildflower garden in the moat--a great break for me after being around so many people. Hardly anyone else was there, just a couple from Australia comparing Australian road trips with the docents. :-)
We enjoyed our time in the V&A. Went to see the glass together then split up to visit the exhibits that interested us individually (husband and I), so we saw what we wanted to see without spending all day there. I think bostonphil7 was probably talking about the Divas exhibit. Didn't see that but did look at the free fashion exhibit below. Then we enjoyed tea and scones in the patio area.
Haven't been to the full Portobello Market on Saturday, but I did buy some antique glass buttons when we visited on a Friday (I think) over a decade ago. Walking around Notting Hill was enjoyable just for seeing the buildings and what people had in their gardens. (We have a picture of a metal gorilla we saw somewhere in that area.)
Thinking about it, we tend to visit places on our own--reading ahead if it seems necessary--rather than taking a tour. I enjoyed all the local tour guides we had on our Rick Steves tour in Italy, but I tend to get impatient (just mentally, not verbally) with people who don't listen to the guide and then ask questions that were covered already! That said, we did overhear a small tour near the Lewis Chessmen in the British Museum last summer, and if you didn't know anything about those pieces, the tour guide helped you understand what you were looking at and was very engaging with the tweens in the group.
So as you said--it's a personal preference really. I love London and hope to visit many more times, so I'm satisfied with just a few hours at a museum knowing that I will probably be back on another visit, and that staying too long gives me diminishing returns anyway. Enjoy your trip!