You are connecting the UNO 5 volt to BLE Vin. That makes me suspicious. You also connect the BLE logic signals directly to the UNO. Is the BLE a genuine 5 volt device? Else You need level shifting for signals going from the UNO to the BLE.
A 3.3 volt device can send signals to a 5 volt device, but not the opposite.
Lots of posting.... Can You tell the Vcc voltage of the BLE?