The answer that we can objectively give for England is according to
administrative district. Here, then, Leicester (329,600) is the biggest with just one station in it, as you note above.
From what I can tell, Sunderland (275,300) is the second largest under this measure, although of course it does have several Tyne and Wear Metro stations. Hull also only has one, but is slightly smaller.
While we're at it, it seems that North Tyneside (201,200) is the largest with
no train stations.
Of course, there are other possible answers for 'place', which could draw form Travel-to-Work Areas, or the '
Primary Urban Areas ' which seem to have formerly been used by the Office for National Statistics but have now been dropped and are maintained as a concept by a think-tank. Under the latter, it would be Sunderland which is the largest with just one station, and this might be the most satisfactory answer as there is clear green-belt land between Sunderland and the nearest locations (Seaham and Gateshead [Heworth]) with stations.