sanderson posted the route:

The Capital Ring is a 78 mile (126km) path around London, linking up parks and green places. It officially starts at Woolwich Foot Tunnel but the circular nature of the path means that it can be started and finished at any place. I have researched an FKT for this path but as yet have been unable to find any record of an attempt. 

Mick Warwick posted about a possible FKT:

The Ribble Way is a 73 mile footpath following the River Ribble along the beautiful Ribble Valley from its mouth to its source. The footpath traverses the counties of Lancashire and North Yorkshire and is divided into 7 sections each approximately 10 miles long.

Sam Anderson posted the route:

The Lee Valley Way is a 53 mile route along the Lee (or Lea) River from its source in Leagrave, Luton to Leamouth at East India Dock, where it runs into the River Thames.

This is a Premier Route. To claim an FKT on this route, you must meet a high standard of documentation and verification. See details here: https://fastestknowntime.com/premier-routes.

Nordkapp is often attributed as the northernmost point in continental Europe (though Wikipedia has a few remarks about that), Tarifa is the southernmost point.  To run between them is roughly 5300+ km.