First of all the lighter the aircraft then the less runway it needs and whilst Lasham's runway may not be so long this aircraft would have been light, without any B737-800 performance data to hand 6 hours does sound pretty imaginable but then perhaps the Russians had a standard issue pencil sharpener to hand!
P.S. That said a fully laden B737-300 could make it off BRS's 6,600ft runway 4.5hrs to LCA so an empty -800 off Lasham's 5,900ft runway for 6hrs isn't so unrealistic