It looks like part of a Matrix screw pitch measuring machine made by Coventry gauges, though its not complete. It should be mounted on a massive cast base with centres.The screw was mounted between the centres and the indicator placed into the thread. The reading was adjusted until the scale was set to the zero line. The whole unit (which was mounted on balls running in a parallel "V" was then advanced using the micrometer causing the stylus to ride up the flank of the thread and back down into the next thread until the scale again read zero and the pitch advance noted from the micrometer dial. This was then repeated until all the threads were measured and any deviation from the correct pitch noted. It was probably made in the 50's or 60's
Having studied the picture again I may be mistaken with the manufacturer. It is a long time since I saw one but it is more likely to be the Pitter gauge unit. It works exactly like the matrix unit but is not quite so sophisticated. The pulley on the back would have had a cord and weight to keep any backlash out of the measuring micrometer.