However, London Fields - Dalston Kingsland no longer appears on
Network Rail mileage file, so you can then no longer actually deduce that the shortest route produced by my tool (which is based on the electronic data) actually matches the shortest route according to Network Rail, which contains data for Crossrail core.
Without a link between London Fields - Dalston Kingsland you need to check which is actually the shortest route according to Network Rail data (the section of Waterbeach - Cambridge and Whitechapel - Abbey Wood - Dartford is left out for clarity as there is clearly nothing shorter).
According to the Network Rail file,
East Coast Main Line from Kings Cross, Cambridge is 58.00, Finsbury Park is 2.50
West Anglia line from Liverpool Street, Hackney Downs is 3.00, Tottenham Hale is 6.00, Cambridge is 55.75 (the line via Seven Sister is longer by 0.50 miles)
Lea Valley line from Stratford, Tottenham Hale is 4.25
Northern City Line from Moorgate, Highbury & Islington is 2.25, Finsbury Park is 3.50
East London Line from Highbury & Islington, Canonbury is 0.50, Whitechapel is 3.75
Crossrail core from Paddington, Liverpool Street is 4.25, Whitechapel is 5.50, Stratford is 8.75
North London Line from Stratford, Hackney Central is 2.50, Canonbury is 4.25
So we can do the calculation.
Cambridge - Liverpool Street - Whitechapel is 57.00 miles
Cambridge - Finsbury Park - Highbury & Islington - Whitechapel is 60.50 miles
Cambridge - Tottenham Hale - Stratford - Whitechapel is 57.25 miles
When travelling down the West Anglia line, there is no possibility to change trains anywhere to another line using only scheduled services (not walking between stations) all the way from Cambridge to Liverpool Street or Stratford, so the shortest route, according to Network Rail, should be the route by changing at Liverpool Street and Abbey Wood. It does not travel anywhere near Canonbury.
However, routes within 3 miles of the shortest route remain valid in the Routeing Guide, and it can contain walks.
A route of Cambridge - Hackney Downs / Hackney Central - Canonbury - Whitechapel is 57.75 miles. It is within 3 miles of the shortest route, so it is valid.