The Jubilee Bridges were opened in 2002, replacing a shabby old walkway that was possibly England's longest urinal. In the mid-1800s, there was briefly a rather splendid suspension bridge here designed by Hatman himself, Isambard Kingdom Brunel; when it was replaced by a train bridge, its chains were reused in Clifton Suspension Bridge. Brunel fan Jeremy Clarkson will approve of such recycling we're sure.
The Jubilees are fun and photogenic to cross. It feels like you're walking along the x-axis of a computer-generated graph, which you probably are.
On the upstream side you have views of the Houses of Parliament and the Eye; at dusk it's a stirring sight, seeing the pods pop with tourist flashes that have little chance of illuminating the opposite riverbank. There are also several street entertainers painted in silver pretending to be automata, an exercise of mystifying commercial success. On the downstream side there's the bustling South Bank.
There are lifts big enough for a couple of bikes (as well as steep stairs) at both ends of the upstream Jubilee Bridge and the south end of the downstream one. So don't shell out £17 for a 'flight' on the Eye: just take the lift up here for that claustrophic-pod feel, and enjoy the views from the bridge instead.
The only access challenge for bikes is at the north end of the downstream bridge. If you don't want to use the steep stairs down to Embankment station, you can get smoothly between the bridge and Charing Cross station concourse, which is on Strand street level, via a narrow concrete walkway at the far left corner of the concourse.
On the north bank from here it's fast and busy Embankment, then up Savoy Hill to Strand. You might cycle swiftly up and down adjacent Savoy Court, sort-of the only place in Britain where you have to cycle on the wrong side of the road.
On the south bank it's a gentle ride along the promenade, accessing Waterloo Bridge by its downriver side up a contraflow cycle lane. Either way, Waterloo Bridge is under half a mile.