Unless you're very lucky, you won't find these pictures on the web. Waimarie's suggestion sounds the best one. It seems that the school still exists but may have moved buildings. If you're no longer in the Runcorn area, you can write to the school at this address:
St Edward's Catholic Primary School,
Wivern Place,
Runcorn,
Cheshire,
WA7 1RZ.
(Phone: 01928 572317).
You could also try to contact other former pupils (or staff), who might have copies of these photographs, through Friends Reunited:
http://www.friendsreunited.co.uk
You might also be able to get one of the local newspapers to publish a letter asking if anyone could lend you their photograph(s). The regional titles, the Liverpool Daily Post and the Liverpool Echo, are both at
PO Box 48,
Old Hall Street,
Liverpool,
L69 3EB.
The Runcorn Weekly News is here:
2 Robert Street, Widnes, Cheshire WA8 6LY
Details of the Runcorn World are here:
http://www.thisischeshire.co.uk/cheshire/runcorn__widnes /newsdesk/
(You can send an e-mail from that page or, alternatively, the postal address is given).
Good luck!
Chris