So I have put the route through RJIS and hkstudent is 100% correct. A Cambridge to London Thameslink ticket is valid to go via Cambridge - Tottenham Hale - Hackney Downs - Hackney Central - Highbury & Islington - Finsbury Park - St Pancras and beyond.
RJIS shows the mileage for this route as 58.8 miles and the route via Hitchin as 58.1 miles. The journey planners can show it in theory if you can get them to force that route.
My bad for expressing doubt, just goes to show that these things should be checked properly before coming to a final conclusion. It still doesn't quite reach Liverpool Street, but is probably the one will get without shelling out for a Travelcard.
I'm equally amazed - thanks for checking it's possible. Whilst I still can't get a journey planner to show this route as valid for a destination of London Bridge, if I instead pick City Thameslink as the final destination, and then "via Dalston Kingsland", I can get National Rail Enquiries to offer me the journey via Tottenham Hale, with the £26.10 single from Cambridge to London Thameslink. For example, at 10:00 on Monday morning, I'm offered:
Cambridge 10:04 to Tottenham Hale 10:59
Tottenham Hale 11:14 to Hackney Downs 11:20
Hackney Downs to Hackney Central (walk)
Hackney Central 11:46 to Highbury & Islington 11:52
Highbury & Islington 11:58 to Finsbury Park 12:03
Finsbury Park 12:08 to City Thameslink 12:21
I assume you'll struggle to get it show that route with London Bridge as the final destination because using the tube will always be faster, whereas with City Thameslink the tube clearly isn't an option.