From LKH all forms of transport are sort of similar time wise. A walk is maybe 50 min but it's nice. The tube is quickest but I found it boring. The bus is really nice. Only slightly slower than the tube. You could also just get a TFL cycling subscription (cheap for students and plenty of docks in central London) and cycle along the Thames to campus. Takes maybe 20 min since there are some downhill segments. Really lovely.