The BJMSP archives going back to the first issue (Volume 1 Part 1 in 1947) are now online for subscribers (including BPS members). It began life as the The British Journal of Psychology (Statistical Section), but became known as the British Journal of Statistical Psychology. Although it changed to the British Journal of Mathematical and Statistical Psychology in 1964 the focus was on mathematical contributions to psychology in its broadest sense (including statistics) rather than narrowly on statistics, though factor analysis dominated in the early years. This was probably partly because of the founding editors (Burt and Thomson) and partly because of the importance of factor analysis at the time.
The first editorial by Burt and Thomson is free to all readers here.