The point in Great Britain furthest from the coast is “just east of Church Flatts Farm, about a mile south-east of Coton in the Elms, Derbyshire” according to the Ordnance Survey in a snippet in this old BBC news article. (Update – featured in a later BBC news article here, and confirmed by the OS here.)
I see another challenge – getting to this point, and then biking from here to the coast. Here is the point, from zooming out, I can see there are coastal inlets that define this point – the Severn Channel near Glocester, the Runcorn near Liverpool, and the Wash near Kings Lynn. I don’t really fancy plowing through Birmingham to get to the first, and ending up in Liverpool will be a long way from my London base, so I’ll probably be heading East. National Cycle Route 63 is pretty much the route needed. Watch this space.