The problem could either be caused by a battery fault or a logic board fault. We had a spare battery in stock and were able to first swap this over and leave the MacBook charging for a few hours. Luckily this has done the job and the MacBook is now fully functional and able to run powered from the new battery pack.
Upon examining the old battery pack, it was apparent that 2 of the cells were swollen and this must have caused complete failure of the battery. Failing batteries with swollen cells are a fire and explosion hazard and should be dealt disposed of in a safe manner.