OK, when I removed the front brake calipers I found that the pads were quite worn yet not to the point here it was a grave situation. I checked the rotors and found they were in very good shape, put in the new OEM pads and re-assembled everything. The groaning sound was gone however, a very small groan could be heard if the ANTILOCK light came on. Before I replaced the pads the groan was quite loud if the ANTILOCK light was on. Now it was barely audible and in addition, it hardly ever comes on anymore. A Mercedes mechanic I spoke to recently told me to replace the horn ring and brushes to remedy that problem. I found that very interesting.
1967 Jaguar E-type Series I, 2+2