How fast you get answers depends on many factors. I just picked up your question but have spent time finding and reading the manual. I am by no means a treadmill expert, but my first thought was treadmill belt tension was too loose to keep the movement sensor happy.
Moving the belt manually would be irrelevant as the electronics would not be monitoring to throw up the E1 Error..
The manual tells you to check all these things.
Loss of Feedback Speed Sensor disconnected Check Speed Sensor
Speed Sensor Misaligned Check Sensor position
Faulty Speed Sensor Replace Speed Sensor
Loose Display Connection Check Display Cable
Faulty MCB (D2 LED on) Replace MCB
Faulty Drive Motor Replace Drive Motor
If BH Fitness are being no help, I would be asking them to take the machine away or get it fixed on-site.
So does the belt turn when you switch it on? Is the belt centrally aligned when it spins?
Page 35 shows belt adjustment and I would guess tension although not specifically mentioned.