Anyway, here's what I came up with - dating back over the past five years, so some of the photos are taken on old point-and-shoots. I started at Richmond, and went east until Tower Bridge, realising that there were indeed quite a few gaps along the way, especially at the west end of the river.
This is the very picturesque Richmond Bridge which dates back to 1777:
Immediately I found that there was a whole swathe of bridges that I'd not photographed - the Richmond Railway Bridge, Twickenham Bridge, Richmond Lock and Footbridge, even Kew Bridge, in spite of having visited the Gardens on a number of occasions. And no Kew Rail Bridge or Chiswick Bridges either.
The next one I managed to track down was Barnes Rail Bridge:
This is Hammersmith Bridge:
I struggled to find shots of Wandsworth Bridge - not the most photogenic - but found this one from 2009:
The next bridge along is good old Albert Bridge, freshly repaired and bright and colourful as ever - here's the photo I took today, which inspired me to put this collection together:
I have a lot more photos of that bridge, taken in all kinds of weather at different times of day (eg the top one, seen at dawn)! The next one along is Chelsea Bridge, which I'm also rather fond of, with its silver rivets. Here's a slightly different view, with my beloved Battersea Power Station in the background:
Heading east, but not far from Chelsea Bridge is the Grosvenor Bridge, carrying the trains south from Victoria station, across the river, past the power station:
Now we're getting right into the heart of London, and the next one along is Lambeth Bridge, again less photographed by me:
list of bridges on Wikipedia helped me out to identify and place the next ones along. First is Blackfriars Bridge:
The next one is much-photographed, by me and everyone else who comes to London:
So, last but definitely not least, is Tower Bridge, probably London's finest:
I don't have any of the Queen Elizabeth II Bridge, right out in Thurrock, so my journey ends here! So, from the thirty bridges that span the Thames from Richmond to Thurrock I'm only missing seven, so not a bad representation of my city's bridges! It's interesting to see - looking at the old and new photos - how much the city skyline is changing, with so many sky-scrapers cropping up to change the view irreparably....