If the HMG procurement team are any good, there will probably be some sort of centralised rebate invisible to end users negotiated directly with E* and other major travel providers.
My last employer (large firm, 100k employees) used BA as the preferred flight partner. To us, it made no sense as - through the 3rd party travel agent - we could only book flights at the same fare as available on the BA website. And these were the fares charged in full to our local cost centres + something like a £15 travel agent booking fee.
The firm, however, received several £m p.a. rebate depending upon total expenditure. ISTR it was in the region of 20%+.
This keeps any discounts secret from the marketplace which makes contract negotiations better/harder depending upon which side of the table you sit.