Interesting, @sarahthecoat - I do like this topic! Yes, there’s a lot of scenes in BBC Sherlock that are associated with the river Thames and its many bridges. I don’t know much about London’s geography either, even if I’ve been there a (small) number of times. But Google Maps is a useful tool. :)
In the Alex Woodbridge case in TGG, I think his body was found on the south river bank, because Sherlock says this to John when they are looking at the fourth ‘pip’ on the pink phone, before they visit the site:
“View of the Thames. South Bank – somewhere between Southwark Bridge and Waterloo.” Which would be a length of about 1.5 km of the southern river bank.
Near the end of TST, when Sherlock is trying to figure out who betrayed AGRA, he’s crossing the Vauxhall Bridge.
Those buildings in the background are on the south river bank, as far as I can see. Right after this scene, Sherlock runs towards them. And then, after Mary has died, he’s walking by the Thames, hard to tell exactly where, and says: “When does the road become a river with only one destination?”
My answer would be: when there’s too much water (= emotions) and the current is too strong. Sherlock’s destination seems to be south of the river. If he reaches Samarra, I think it’s likely that Sherlock will be ‘killed’ (by Love) and end up on the ‘south bank’ (with free love) like Alex Woodbridge. And I don’t think Samarra can be avoided.
In TLD, when Sherlock writes his little message to Mycroft’s monitoring guys, he’s walking with Faith in Soho, near Oxford Circus and Picadilly Circus.
They keep moving southeastwards. I believe the bridge they’re crossing after that is one of the Golden Jubilee Bridges. That’s actually a triple bridge with two pedestrian bridges on the flanks and an older railway bridge (Hungerford Bridge) in the middle.
And the park by the river that Sherlock and Faith/Eurus are visiting at dawn, and where Sherlock is having his breakdown, is the Jubilee Gardens, at the south bank of the Thames close to the Golden Jubilee Bridges. (Well, since the river is meandering, Jubilee Gardens is actually on the east side, but in general this should belong to the south side of the river). The bridges are located about 2.1 km north of Vauxhall Bridge and 1.2 km southeast of Piccadilly Circus. It’s also very close to the London Aquarium and the famous ferris wheel London Eye (both on the south side).
I also seem to recall that Culverton Smith says that “we must be careful not to burn our bridges”. So yes, it seems like you’re right, @sarahthecoat; the river is a threshold.