The answer given to this question is correct, but Gloucestershire do have a claim to have been County Champions on more than one occasion.
Before the start of the official County Championship in 1890, a 'champion county' was chosen by the press each year. At first it was the team with fewest defeats that was awarded the championship, but by the mid 1880s a points system was being used – usually one point for a win and half a point for a draw. ESPNCricInfo lists eight sources of nominations, of which up to six made a choice in any one year; and unanimity was by no means a given.
Records of nominated champion counties go back as far as 1825.
Gloucestershire were unanimously named as champion county on two occasions: 1876 and 1877. They were named as champions by one or more sources on two further occasions (1873 and 1874). In 1873 they were named as outright champions by just one source, but four others (out of six) nominated them as joint champions with Nottinghamshire. In 1874, four of the five sources nominated Gloucestershire as outright champions; the fifth went for Derbyshire.
Gloucestershire's success in the 1870s was of course due in no small part to the efforts of one man: W. G. Grace. 'The Doctor' played for the county from 1864, and played his last first–class match in 1908 (when he was 60 years old). He was in fact one of the sources quoted by CricInfo for naming the champion county; but any accusation of bias is wide of the mark, as in 1873 he was the only source that went for Nottinghamshire, rather than Gloucestershire or both jointly.
Despite the above, Gloucestershire have indeed never won the County Championship – which is a competition that started in 1890 – so (as also stated above) the answer given to the question is correct.
Neither Somerset nor Northamptonshire has ever been champion county or won the County Championship.
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