The A1261 is located in East London at the northern end of the Isle Of Dogs. It consists of West India Dock Road and Aspen Way (including the East India Link Tunnel).
Westferry - Canning Town
This is the main road that runs just north of Canary Wharf - but signposting can be confusing. Traffic coming from the A13 Commercial Road will see a sign to the right indicating Docklands / Isle of Dogs A1261 in a white box suggesting it is non-primary at this point. At this junction the A1205 Burdett Road is to the left and straight ahead is the parallel A13 which follows the route of the A1261 albeit slightly further north. The two roads are called East India Dock Road (the A13) and West India Dock Road (the A1261). The former keeps its name for longer, so it does end up further to the East for its most part.
West India Dock Road is a short dual carriageway, ending where the carriageways split for the A1203 Limehouse Link Tunnel to merge into it. In between you have Westferry DLR station and the A1206 Westferry Road, which takes you to Canary Wharf and round the whole of the the Isle Of Dogs (we'll meet it again later). Another slip-road of the Limehouse Link Tunnel terminates on that road.
There are green signs during the entirety of this stretch suggesting that the A1261 is primary, though only online maps such as Openstreetmap actually show it as such!. Certainly this section of road (unlike the rest) is not part of the TfL network.
Blackwall-East India Dock Tunnel(A1261)
Once the A1203 Limehouse Link Tunnel has merged in the name of the road is Aspen Way. There is a slip-road to the eastern branch of the A1206 (Cotton Street and Preston Road), which also provides access to the A102 Blackwall Tunnel and the A12. Also you can use this junction to U-turn on yourself, of course, which you may want to do if you want to enter Canary Wharf via the Upper Bank Street entrance, and you can also get to Billingsgate Fish Market from this roundabout.
For those remaining on Aspen Way, we go over both Blackwall Tunnels, then the next junction is your choice whether to exit for the A1020 Leamouth Road / Lower Lea Crossing. For traffic that wants the A12, using Leamouth Road and the B125 Abbott Road provides another route out, and you can also approach the Blackwall Tunnel from the east this way, although that option usually proves to be just as busy as any other.
Remaining on Aspen Way we head back in a northerly direction through the East India Dock Tunnel to meet up with the A13 again; in fact the A1261 has the mainline whilst the A13 takes the slip roads here, especially in the other direction when leaving the junction.
It would appear they maybe wanted to re-route the A13 via this route, and possibly even through the Limehouse Link Tunnel too. In any case most of the main traffic will be using this route.