Only holders of Freedom Passes (which are only available to senior citizens living in London) get free Tube travel. An English Bus Pass, issued elsewhere in the country, is only valid on London buses. (Bus passes issued in other parts of the UK aren't valid). Note that, as long as the bus has the London Transport roundel on it, there are no time restrictions for free travel with an English Bus Pass.
A Senior Railcard isn't valid for directly purchasing Tube tickets on their own. However if you're travelling into London for the day, you can get a Travelcard (for unlimited travel on buses, trams and the Underground, the DLR and some National Rail services) added onto your rail ticket and, if you use a Senior Railcard, the one-third discount is applied to the cost of the Travelcard as well as the rail journey into London. (There are minimum fare requirements for that to apply. See link below).
Further, if you've got an Oyster Card for travelling in London (which has to have been registered in your name), you can get your Senior Railcard linked to it, so that you get a third reduction on off-peak Underground and DLR fares:
http://www.senior-railcard.co.uk/help/faqs/143/