Rather than source a new AC/DC power supply for the BCS and the relay board I have found a cheaper option: an old cell phone charger. The one I have is rated at 5vDC 890mA.
I think I will use the cell phone charger for the board and use the power supply that came with the BCS for the BCS. It just so happens that I bought two of these power entry modules:
So all in all these things and the two power supplies shouldn't take up too much space inside the enclosure.