There are definitely corp negotiated rates with BA for Concorde service. The price level you talk about seems reasonable. Although I won't disclose the fare here (I think it's confidential), we have a very favorable rate for F and J on BA.
Generally, to book those rates, you must book directly through your company's travel department - which most companies will only do for employees on business, clients, and sometimes employees and family on holiday.
If you work at a big company, you might want to inquire with your own travel department.