Yes, I think Cotswold may have sent theirs(about a dozen) as they don't have them anymore. Colchester used to have a tiny group(about 3) so could have sent them to West Midlands too.(will look on ISIS)
West Mids have a good big Blackbuck herd- forty or fifty of them..
Colchesters blackbuck came from Marwell in around 1983
I believe some of Howletts original Asian deer/antelope came from a private collection near Maidstone owned by Sir Gerrard Twirrhyt(?)-Drake.