From the Wikipedia page List of crossings of the River Thames
In London, there are 33 bridges that cross the River Thames and one proposed bridge, in order from west to east are:
- Hampton Court Bridge
- Kingston Bridge
- Kingston Railway Bridge
- Teddington Lock Footbridge
- Richmond Bridge
- Richmond Railway Bridge
- Twickenham Bridge
- Richmond Lock and Footbridge
- Kew Bridge
- Kew Railway Bridge
- Chiswick Bridge
- Barnes Railway Bridge
- Hammersmith Bridge
- Putney Bridge
- Fulham Railway Bridge
- Wandsworth Bridge
- Battersea Railway Bridge
- Battersea Bridge
- Albert Bridge
- Chelsea Bridge
- Grosvenor Bridge
- Vauxhall Bridge
- Lambeth Bridge
- Westminster Bridge
- Hungerford Bridge
- Waterloo Bridge
- Blackfriars Bridge
- Blackfriars Railway Bridge
- Millennium Bridge
- Southwark Bridge
- Cannon Street Railway Bridge
- London Bridge
- Tower Bridge
- Thames Gateway Bridge (proposed)
The TfL page on river crossings is [1].