Go down the A12 to the M25 and either go M11 or A13 it’s swings and roundabouts really. Take the A13 through to Canning Town flyover and keep to the middle lane for the East India Dock Tunnel and then Limehouse LInk (30mph with several cameras) follow the Highway and advice as above.
Blackwall Tunnel has tidal flow operation meaning 3 lanes heading North, 1 South in the morning and can be sticky. Once through the tunnel its dual carriageway up to the point where you trun right for the A2. It is then a slow drag in through Deptford and New Cross and doesn’t get much better. Then you’d have to cross back over. It’s too much of a ballache to be viable.
From home in Chelmsford or work in Harlow I’d go this way as there are no nasty surprises and it is a fairly decent straightforward route.