Secret service is your best bet. I tried e-mailing myself & got this answer :
Thank you for your recent e-mail.
It was great to read of your interest in 'Filthy Rich and Homeless' on 24 May.
However, due to limitations of time and resource, we are unable to conduct the further research necessary to provide correspondents with details of incidental music used in programmes.
I appreciate that this may come as a disappointment but the expenditure to do this could only come from the licence fee, resulting in resources being diverted from the primary function of the BBC, which is to provide programmes.
typical BBC