16 fire engines and nearly 100 fire fighters were called upon to tackle the blaze after receiving the call at 11.11am.
It took over four hours to get the fire under control, with support being called in from neighbouring fire and rescue services.
Eventually, the fire was extinguished by 3.30pm.
Beds chief fire officer Paul Fuller said: “Incidents like this show that even the most modern buildings can still suffer from major fires.
“The building’s sprinklers protected the main part of it but it is a reminder that there is still the need to maintain fire safety in even the most contemporary buildings.
“I’d like to extend my thanks to colleagues from Buckinghamshire, Hertfordshire and Cambridgeshire for their support during this incident.”
A fire investigation is still inderway.