I thought it was Turner Group who were the principal construction contractors:

http://www.hays.com/jobs/mia/index.html

Maybe Baytur just did the stone work - that's all their website takes credit for:

http://www.baytur.com/projects/gbp_26.asp

Tallg, next time you get close to the museum, take a very close look at the stone cladding on the building. I don't think you'll be congratulating anyone for the workmanship.