As part of Corporate deals BA offer discretionary cards. There is a pretty strict formula to the number and type of discretionary are granted.
Normally BA ask their company (or travel agent) contact to allocated the discretionary cards [Account Manager], but it is possible to bypass that, although any cards given will always be part of the overall allocation.
Each year BA produce a report for each company of their discretionary card holders and give them the opportunity to review the allocation.
With the demise of ECCCAs in July, the number of discretionary cards will be drastically reduced [I don't know if it is still true, but I once heard the figure of 1,050 Prems; 26,000 Golds and 78,000 Silver discretionary cards issued as part of ECCCA's or their overseas alternates - there was apparently once as many discretionary Golds are earnt Golds].
In addition BA have periodically given an allocation of discretionary Golds and Silver invites to major travel agents for allocation to their customers. These cards are issued on a once only basis and are never renewed. I don't know if this practice has been withdrawn.
Customer Service can also upgrade EC memebership levels, especially as part of the HLC procedure.