Yep, that's my commute pretty much.
Barking - A1306 to Rainham (quite a bit of cycle paths), turn left at the Police Station into Upminster Road North.
Continue into Warwick Lane
Continue into Bramble Lane
Just before the M25 bridge, quick left into Pea Lane, right at the end of Pea Lane into Ockendon Rd
Right into Clay Tye Rd then left into Fen Lane.
Continue to end of Fen Lane through Bulphan then cross the A128 (dog leg - right left) into Doesgate Lane
Right at the end of Doesgate into Lower Dunton Rd then left into Old Church Hill (this is steep, trust me!)
At the top of Old Church stop for a breather then turn left and then right into Dry Street
All the way down Dry Sreet turning left at the bottom onto Nether Mayne to the roundabout
From the roundabout take the London Rd all the way to Southend
If you don't want to touch the A13 the alternative (and my most frequent way) is through Dagenham, Hornchurch, Upminster, turning right into St Mary's Lane then right into Clay Tye Rd where you can pick up Fen lane.
Hope that helps!