I stumbled across a really useful list of UK central government Twitter accounts. I felt these may well be very useful for you. I've checked them all to ensure they work, but if for some reason you spot something which does not function please add a comment below and let me know.
BIS
DFID - http://twitter.com/dfid_uk
No 10 - http://twitter.com/downingstreet
DCSF - http://twitter.com/dcsfgovuk
MoJ
UKTI - http://twitter.com/UKTI
Directgov - http://twitter.com/directgov
Businesslink - http://twitter.com/BusinessLinkGov
NHS Choices - http://twitter.com/nhschoices
COI
EHRC - http://twitter.com/ehrc
Ofcom - http://twitter.com/ofcom
Cabinet Office - http://twitter.com/cabinetoffice
Cabinet Office – Director of Digital Engagement - http://twitter.com/DirDigEng