Logging back on to say definitively that you can get to Brandon with split ticketed off peak or anytime returns, don't pay £45.
Absolute cheapest is LST-CBG, CBG-ELY, ELY-BND. Change at Cambridge or Cambridge North. £24.80
2nd and slightly easier is LST-CBG, CBG-BND, and you can just change at Cambridge. £27.20
Both of those you're restricted to Greater Anglia trains.
Fastest is KGX-ELY, ELY-BND. £31.20
I believe you can get on at Tottenham Hale with a ticket from LST becuase breaking your journey is allowed, but I'm less clear on that.