One tends to feel that Great Britain's many coastal nooks and crannies indeed offer a fair number of potential grey areas as to what is, or isn't, the sea. For instance, re the Bristol Channel as cited by clappers: the River Severn estuary which becomes the Bristol Channel, goes -- narrowing as it does -- a long way in the opposite, inland, direction. West of what point, does this body of water qualify without doubt, as "the sea"? -- as with clappers's musing about Minehead. (Weston-Super-Mare, as per its name, clearly considers that it ranks as a seaside place.)
Re DarloRich's "74.5 miles": I find that the Ordnance Survey opines that Great Britain's furthest point from the sea is a little less than that distance, therefrom. O.S. offers in this context, a location just outside Coton in the Elms, near Burton-on-Trent -- giving as 70 miles, its distance from the sea: "the sea" being defined here as the most south-westerly point of the Wash, not far from Boston. Again, opinions are likely to differ as to where this particular marine inlet becomes, indubitably, the sea proper...