Modelman
Whilst FD is absolutely right I think you need to put a couple of things in perspective, you must absolutely do what you feel most comfortable with, your QCC is an exciting time but on the other hand don't do something that is outside your own personal limits, talk to your instructor to see what he thinks. On the other hand if you do as FD says then you can route direct to Gloucester overhead Lemmington Spa, then split Wellesbourne & Snitterfield in half, when you cross the other side of Lemmington you can climb to 3,400ft and still be under the B'Ham CTA, but make sure you are clear of the B'Ham CTA that is 1500ft - FL45 before climbing. Then make sure you are above 2,200ft for the Restricted area R204, I have not got my map to hand but this could be a restriction for heli's only? check your chart legend.
Then when navigating to Connington you could go virtually in a straight line using Banbury & Northampton as visual reference points, I don't see any need to go overhead Cranfield, this just seems a tad out the way.
Just remember to stay relaxed, plan ahead, think ahead, and if you get into any bother just tell ATC and they will help you out, and above all,
ENJOY IT!! 
it will be the best flight you have ever done, beating your 1st solo by miles, let me know when you are due at Gloucester, I'll shout you a drink (ahem, non alcoholic of course) in The Aviator
Dean