How can a person be convicted entirely on the word of another person without any supporting evidence?

In criminal law (UK) I have been studying Miscarriages of Justices and I am alarmed and appalled at the number of cases where convictions have occurred on the say so of a solitary alleged witness.It is my understanding that in criminal cases the burden of proof is greater than that of civil cases which is based on the balance of probabilities.In a case of one word against another with no other supporting evidence the balance of probabilities can never be greater than 50/50.So why are there numerous convictions and MOJ's?Surely it should be made compulsory to for both accuser and accused to take independent lie detection tests or similar? This would save court time and costs for all concerned and weed out false allegations.Any comments or case history details would be appreciated.