You can get a cab back to Cambridge for around £80 on Uber so if there are 4 of you its not a complete nightmare either.....
Just out of curiosity, do trains not run out of London through the night if you are going out in London from say Cambridge for example? I only ask because 45 minutes seems pretty close as I grew in Long Island (about 50 minutes from New York City) and we were always able to get home all hours through the night
Most of the trains etc stop from say 1am - 6am and then they ramp up into the normal day routine. Depending what kind of night you're heading too - 6am probably wont be a problem!!