I think if you only want to carry one card then Visa is the better bet.
Cash points may be quite rare though, on this route - it really does avoid sizeable towns.
St Neots, Wragby??, Barnard Castle??, Alston??, Innerleithen??, Lincoln on the way back.
From memory: Cheshunt (several, plus small supermarkets), Gamlingay (cashpoint by Co-Op on left when entering village), Bourne (detour), something on the edge of Sleaford, 24h Somerfield at Petrol Station in Thorne (I think it's on the route), petrol stations north of Thorne, Howden (short detour into town centre), Thirsk (small detour), Scotch Corner services (short detour from Middleton Tyas), Barnard Castle (detour onto High St), Alston (several at bottom end of the town), Brampton, Longtown (next to Co-op) plus petrol stations, Langholm (petrol station), Innerleithen (shops and atms), Dalkeith (several).
I used most of these as proof-of-passage on my DIY ride of the L->E route.