You need to read the information in the merchant navy guides at the National Archives at
http://www.nationalarchives.gov.uk/records/atoz/m.htm On the link you gave, scroll down to the block of 4 images associated with Joseph Samuel Mayor’s, part of your answer is in the text under them; yes all in that series have photographs.
Look at the image with his photograph and you will see 2 numbers with dates; those numbers are ship’s identification numbers as per the Lloyds register – there’s a link to CLIP and there you can convert those numbers to vessel names and descriptions.
Using the two examples in that image 139626 & 125756
From
http://www.crewlist.org.uk/index.html > Clip finding aids > ships > ships by ON
Enter the numbers 139626 = PROMUS; 125756 = COURTOWN
There’s lots of information about where more records are held and more details about the ships in the images.
You’ll also see a finding aid for people too.