My friend and neighbour and all round countrywoman tells me that the sound I heard was a Muntjac deer. Check them out on YouTube. Not native to the UK but introduced from China into Woburn Park by The Duke of Bedford in the 20th Century, they have escaped and multiplied in the wild and we see (and hear) them regularly. They are known as the barking Deer because of the noise they make and they breed all year round.
I am glad that the noise I heard was a deer and not another fox – after the carnage wrought recently amongst the poultry by a visiting Reynard.