Downriver from Southwark Bridge is London Bridge. Often confused with Tower Bridge, it is actually central London's most characterless crossing: a gum-chewing, slack-jawed, adolescent concrete shrug that links Southwark Cathedral on the south bank with Monument on the north. It's a fast, wide road - the A3, in fact - without much to recommend it, except for a fine views downriver of Tower Bridge, especially under evening sun.
It dates only from 1973, and is the latest in a line of constructions on the site. Medieval London Bridge lasted 600 years. To the delight of tourists and locals alike, it featured shops, houses, and a regular display of severed traitors' heads.
Its 19th-century replacement, designed by Rennie, proved inadequate for the weight and volume of traffic. It was sold to a US entrepreneur in 1968 (he didn't think it was Tower Bridge, as an urban myth claims) and now graces an artificial lake in Arizona.
From here you can go right along the riverfront on both north and south sides. North access is past Monument and down Fish St Hill, from where it's stepless (and technically a footpath, so use good judgement) all the way to Tower itself. South access is left along the main road and left up Hays Lane to join the riverside path (again a footpath, again good judgement) past The Scoop (which often has free outdoor entertainment) and the ovoid City Hall. Either way, Tower Bridge is about half a mile away.