The bank’s former chief executive was responsible for running up the biggest corporate loss in British history and his apology came when he met shareholders for the last time before resigning in October 2008.
The footage will be shown on BBC One Scotland tonight in the documentary ‘RBS: Inside the Bank that Ran Out of Money’.
In it, Goodwin responds to a call from one investor, Mr Blackie, to apologise.
He says: “Well, Mr Blackie – wouldn’t want there to be any doubt. I am extremely sorry.
“I echo the sentiments and – I am extremely sorry, extremely sad to be leaving the company at these extremely difficult times.
“There can be no question other than that I am extremely sorry.”
The documentary will also assess the bank’s involvement in the US sub-prime property market and its pursuit of the Dutch-based banking group, ABN Amro.