We live in Nottingham and have tried every combination. If you are flying into Heathrow, the coach, National Express, is by far the fastest and most economical option. The coach will pick you up at terminal 2 or 5. The biggest downside to the bus is that the bathroom is usually unusable, so you must prepare! It takes between 2.5 hours to 3 hours.
If you go through the center of London and then up on East Midlands trains, it will take you at least 50 minutes to get to St. Pancras--however you do it. Then you have 2.5 hours on the train, which runs hourly until about 22:30. The trains are a little bit more comfortable, but if you are going on a peak hour, I'd recommend getting a seat reservation. Purchasing a ticket online, three days in advance, will cut some costs. If you are travelling mid-day, you could order your ticket through
www.megatrain.com (three days in advance) and save a lot of money.
Flying into Manchester and taking the combination of trains from there will take at least 3.5 hours to Nottingham. Each way involves transferring at least once. The more north you go, the more prone to flooding...so it could take longer from here as well... I'm not choosing the Manchester option anytime soon again.
So, with luggage, I'd do National Express. Without luggage and the ability to meet a friend for lunch in London, I'd do the train.