Connection at LHR on return from NRT

Hello there, first post, amazing group 
Later this year I'm flying with VS to Tokyo and back. No worries for the trip there, or the connection at Heathrow, but I am a little concerned about the return leg.
Flying back to the UK, I should arrive at about 3.45pm and will have over 4 hours to kill before getting on a BMI flight to Teesside. The last time I did this (returning from LA) I had a much shorter wait but was *out of my mind* because there was very little in the way of anything to see or do in the UK departure lounge in T1. I was also extremely tired after an overnight flight.
I feel a prat for asking this, but is there anywhere you can go to sleep (as there are rooms you can rent at Narita for these situations), or even a way to get to the more interesting parts of Heathrow, even though you are a connecting passenger?
Best wishes
Paul

Later this year I'm flying with VS to Tokyo and back. No worries for the trip there, or the connection at Heathrow, but I am a little concerned about the return leg.
Flying back to the UK, I should arrive at about 3.45pm and will have over 4 hours to kill before getting on a BMI flight to Teesside. The last time I did this (returning from LA) I had a much shorter wait but was *out of my mind* because there was very little in the way of anything to see or do in the UK departure lounge in T1. I was also extremely tired after an overnight flight.
I feel a prat for asking this, but is there anywhere you can go to sleep (as there are rooms you can rent at Narita for these situations), or even a way to get to the more interesting parts of Heathrow, even though you are a connecting passenger?
Best wishes
Paul