The history of how the lines were built appears to make the mileages complex, but start here:
http://www.railwaycodes.org.uk/elrs/_mileages/e/ecm7.shtm
My interpretation of the mileages is
Benton North Jn is at BNE 0m0ch.
Earsdon Jn (former?) is at BNE 2m53ch, EJM 7m08ch
Bedlington Jn is at EJM 15m68ch, BWC 0m0ch
Ashington (new station) is given on that site at EJM 2m72ch
So 2m53ch + 8m60ch + 2m72 ch = 12m185ch, or 14m25ch.
Railway codes website gives the EJM Mileage as a continuation of the BTN ELR mileages, with a datum at the former Manors Jn, and the mileage measured along what is now the Metro line via West Jesmond and Benton.