I have to go to Coventry in a few weeks to go to a trade fair. I looked up the rail fares and discovered that they can be astonishingly cheap – typically around £12 each way, provided that you book in advance. However, some of these fares take you via London and therefore provide for a cost-effective way to travel to London at peak times if you can book in advance. Simply search for fares from Cambridge to Coventry and specify “via London King’s Cross”, and you’ll often find you can travel on the 0715 or 0815 to Kings Cross for £12, and likewise return on the 1745 or 1843 for £12, which would normally attract a full fare of £38.60 return, saving you £12.60. You do have to travel on those specific trains though! If you have a nationally-valid railcard (i.e. not a Network Card) you can get a third off the already-discounted price, too. The trick also works in First Class, where you can pay £34 each way on that same routeing.
If the Coventry fares have sold out, you can also try booking to Rugby, which is technically a different ticket but is charged at the same price.