heathrow to central london:

15 min £16.5 by heathrow express, or 50 min £4 by tube (underground).

you may take piccadilly line from heathrow to green park and have a wander about buckingham palace and parliament square...

london to loughborough approx 1 hour 30 min by train (time and fare see link below):

http://ojp.nationalrail.co.uk/en/pj/tt