I have called up IND, HO twice and they were extremely helpfull and co-operative. Their local number is a premium number (0870 606 7766) and is open 9 to 4 Monday to Friday. I am not sure whether you can dial this number from overseas (since its a premium number i.e. about 10p per minute is charged to your phone bill). Their email response is also excellent. They replied to my enquiry within 2/3 hours (
indpublicenquiries@ind.homeoffice.gsi.gov.uk).
They, however, do NOT reply to case specific querry or on progress of your application. I see no purpose of calling them up just to know about the status of your application. Its a waste of time on both the sides.
I havent had a good experience with work permit section. Their phone is either busy or out of order (0114 259 3776). They also dont reply to your emails.
For all the contact details, best place to check is their website. One thing I like about IND and HO is that they update their website regularly and the information contained therein is quite relevant.