It all began in 1582 when Pope Gregory XIII ordered a change of calendar from the Julian (named after Julius Caesar), which had been in use since 42 BC to the Gregorian.
The Julian calendar, which consisted of eleven months of 30 or 31 days and a 28-day February (extended to 29 days every fourth year), was actually quite accurate. After centuries, though, even a small inaccuracy like this adds up. By the 1500s it had put the Julian calendar behind the solar calendar by 10 days.
However, the British did not make the change in 1582, so there was a difference of 10 days between the calendar in Britain and the rest of Europe.
By 1752 the difference had increased to 11 days (one calendar had a leap year in 1600, the other did not). Even the British realised that something must be done and they changed to the Gregorian calendar in that year.
Until 1752 the tax year in Great Britain started on 25th March, old New Year’s Day and Quarter Day. In order to ensure no loss of tax revenue, the Treasury decided that the taxation year which started on 25th March 1752 would be of the usual length (365 days) and therefore it would end on 4th April, the following tax year beginning on 5th April.
The next difficulty was that 1800 was not a leap year in the new Gregorian calendar but would have been in the old Julian system. Therefore the Treasury moved the tax year start again from 5th to 6th of April, and this date has remained unchanged ever since.