Separate records held for England and Wales also show the heaviest rainfall since they were started in 1766.
Regional records have also been beaten, with the flood-hit South East of England getting well over double the rainfall expected in a normal winter, the BBC reported.
The persistent string of powerful storms and heavy rain brought extensive flooding to parts of the UK.
About 6,500 homes have been affected by flooding since December, with many people forced to evacuate their homes.
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The south-east and central southern England had already broken the winter record on 11 February with a total of 439.2mm. The previous record had stood since 1914-15.
According to the England and Wales precipitation records, some 435mm of rain fell this winter, beating the previous highest total of 423mm also set in 1914-1915.
A Met Office statement said: "We have seen some contrast between the south and north of the UK, with northern Scotland having received a third more rainfall than its long-term average in contrast to the almost two and a half times seen in south-east and central southern England.
The mild weather means the UK is also on target for its fifth warmest winter since records began in 1910.
The average temperature over the past three months was 5.2 Centigrade, about 1.5 Centigrade higher than the typical winter.
The latest UK-wide figures also show the heavy rain in February led to south-east and central southern England receiving 133.3mm, almost two-and-a-half times the monthly average.
The flooding caused widespread disruption to travel services, including damage to rail services in the west country, and has impacted on local business and tourism.