The A2204 must be one of the stranger A-roads: only a couple of hundred yards long, unsigned and S4 throughout. It starts at a roundabout and ends in a river (or at least on a slipway)!
It is the approach to the Woolwich Free Ferry on the southern bank of the River Thames, which crosses the river to meet the A117. It is not clear why this road didn't become part of the A205 when the South Circular road was created.
The A2204 in 1923
It seems from the 1923 MOT map that the A2204 number has always been the link from the A206 to the Woolwich Ferry. Originally it was the short section of Hare Street between Woolwich High Street (the A206) and the ferry pier, with the number presumably moving to the present pier when the latter was built in the 1960s; the old road is now lost under the Waterfront Leisure Centre. As the dual carriageway section of the A205 up the hill from the ferry was built at the same time it is even more strange that the number survived.