ianobi,
yes, you were right. My PSTN service provider (Sky) was not forwarding CallerID to my home phone line. At the moment Sky advertise CallerID service as free of charge, i.e. included in the Line Rental fee, but in my case it was not activated. I tried *#234# and it confirmed that. Then I called Sky and asked them to fix this, which they did and everything works fine now.
Thank you for your help and advice.