Presumably you mean the furthest you can go before you start coming back in which case it doesnt matter where you start from the distance is the same. The circumference of the earth is just under 25000 miles (slightly less pole to pole) so half that would be your answer
The most northerly part of the UK isn't quite Muckle Flogga, but a rocky islet just to the north-east of it called Out Stack. Amazingly, Mark's link recognises the name.
Should have added - the farthest distance from Out Stack is 20020km or 12440 miles, (+/- 0.3%, since that calculation is based on the Earth being a sphere, whereas it's an ellipsoid with bulges and flatter bits, so getting the exact surface distance is not easy).