To be ignored or shunned.
The origins of this phrase aren't known, although it is quite probable that events in Coventry in the English Civil War in the 1640s play a part. For those not familiar with the UK, Coventry is an industrial city in Warwickshire, England. It is well-known for its two cathedrals; the modern cathedral being built in 1962 to replace the old cathedral, which had been destroyed during an intense German bombing raid 1940.
In the 17th century, when this phrase is supposed to have originated, Coventry was a small town. It is suggested that the phrase, although we now use it in an allusory sense, originated from people being actually sent there.
The story - and it is no more than that - is that Cromwell sent a group of Royalist soldiers to be imprisoned in Coventry, around 1648. The locals, who were parliamentary supporters, shunned them and refused to consort with them.
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