It sounds like an overuse-type achilles tendon problem, Foxy. Although tendinitis CAN be felt in the midline, it's often to one side or the other depending on where the gastrocnemius or, much more rarely, soleus fibres have become stretched and torn where they are attached to the tendon.
The standard treatment is reducing your mileage by about a third (or to whatever you can do comfortably), ice, anti-inflammatories if it's bad enough to prevent you from walking normally, and a gait assessment to see whether you need a different type of shoe. You're well due a new pair anyway, if only to rotate with the Reeboks (I didn't know Reebok did proper running shoes - doh!) to vary the biomechanical stresses.
Hope you're soon on the mend!
Tim, when your sprats are big enough to demand clothing with labels, you will bitterly regret having denied yourself the luxury of lots of pairs of delightfully expensive running shoes.
Cheers, V-rap.