Route for me and A2:
Oxford Circus

White City

run to Wood Lane

Hammersmith

Acton Town

Earl's Court

East Putney

Clapham Common by 37 bus

London Bridge

St. John's

New Cross

run to New Cross Gate

Whitechapel

Liverpool Street

Clapton

Hackney Central by 106 bus...
At this point the NLL troubles kicked in and the rest of the route was heavily improvised...
No trains at Hackney Central, so

Canonbury by 277 bus and a short walk

Highbury & Islington, no westbound trains

King's Cross St. Pancras

St. Pancras International

Farringdon

King's Cross St. Pancras

Caledonian Road

walk to Caledonian Road & Barnsbury

Highbury & Islington
Both A2 and I were staring at the map bewilderedly, so we decided to team up before heading through the ticket barriers at Oxford Circus. I'll gloss over some initial indecisiveness that saw us at Holborn before doubling back westward on the Central Line.
No District line train in sight at Hammersmith but a Piccadilly line train was in the platform so took that to Acton Town, but just missed the District back and had to wait ages for the next one. In the meantime we met Myles. After Putney Bridge, Myles took a different route to Clapham Common, but it made no difference as we all subsequently got off the same Northern Line train at London Bridge.
Good double back at St. John's and we then left Myles behind on the run to New Cross Gate. Minor delay on the way to Whitechapel as someone had tripped the emergency alarm. At Liverpool Street A2's ticket didn't work and he had to also produce his railcard. Fortunately we had plenty of time. Also, I was loitering by the wrong platform but A2 put me straight (if I'd been on my own I probably would have been on the wrong train).
On to Clapton then bus to Hackney Central for a train towards Kentish Town West. 'No trains, mate!' cried a passerby as we headed up the ramp at Hackney Central. What a portentous cry! After checking with the staff member we went to get a bus to Dalston Junction, and a 277 came by and A2 established this went close to Canonbury, so we headed there and got a train to Highbury & Islington. We missed a random NLL(-ish) train at H&I by seconds that would have got us to Caledonian Road & Barnsbury and probably to Camden Road, but there was no sign of any other trains: the display boards said 'Service Suspended' and the staff member had no information. We therefore headed towards St. Pancras International.
We figured we'd go back to Caledonian Road & Barnsbury and either we'd get a train or would take a photo of the 'Service Suspended' signs and call it a day. Fortunately a train arrived just as we got there and we finished at H&I.
(I couldn't stay long at the pub and I owe 50p.)