If you have a bus pass issued by another English council, you can use it to travel free on London buses.

Yes you can if it is an OAP or disabled pass issued by an English council. However you cannot use it on the Underground or rail system in London

Each country the old age pass applies to MOST services.

So an English pass will work on normal London busses. Not sighteeing tourist specials though.

If if you mean the OAP bus passes, then yes. I have with no problem.