I highly doubt you'd be successful. For one, you'd need to prove you were actually planning to use the bus to get to / from /within Central London, and I think that there's going to be a real issue there to prove you didn't want to take the Tube to begin with.
Secondly, if they were to accept your claim for a difference refund, I think that others who'd try the same as you, either one of all of you would mention this somewhere, and the word would spread. And before you know it, everybody who used the Tube - but in normal days 'could' have used the bus - would be trying it on.
So only if you have proof you make the exact same bus journey every day, and this is all logged in your account, I'd say they might be lenient. But I don't believe there really is much legal ground for this, although I'll be happy to be corrected. I just haven't ever heard of this in times of bus disruption before.