You could get there as early as 1003, 1023 or 1123 via London, but the rail industry doesn't want your custom for this journey so it's best to use another mode of transport.
According to the Train Companies, passengers either wish to take a direct train or the shortest route. They are in denial that passengers actually want the quickest route or appropriate journey times to suit their requirements, and therefore do not always cater for such requirements.
If you do go via London, then you'll need to "split". Manually. This will cost £17.90 for Peterborough-London (book on the East Coast website for the best deal) and £20 (or £23 first class) from London to Coventry. I'd walk from KGX to EUS; it should take 15 mins max, but you need to allow at least 35 for it to be a valid connection.
Trainsplit.com will be able to work out such splits for you automatically in future, but not at present. Some people in the rail industry appear to be against split ticketing websites, despite the fact that such websites might actually encourage people to travel by rail for such a journey where the conventional booking engines will just say it can't be done.
Is there any other industry that so actively puts off potential customers? (rhetorical question! Of course there isn't!)