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Ben689908
Coincidentally I am sitting here doing some maps programming with turf.js. It will solve this problem with its circle function, which actually returns a polygon defined by a number of points, because GeoJSON does not support an actual circle. I've put the code in a JSFiddle, if you run it you should get the coords in a block of GeoJSON:
https://jsfiddle.net/j7oef1c5/3/
You can copy that into https://geojson.io/ to check it looks ok, it should look something like the attached. Even tho it is approximating a circle presumably the vertices fall on what would be the circumference, so it should be right?
Are you planning a festive bike ride?
EDIT: just realised I made London Bridge the centre, not the 6 o'clock position. I guess the way to fix this is to start with the coord for London Bridge, move it north by the circle radius to get the center, then go from there
EDIT2: edited the fiddle with the fix above and updated attached image