Before the Gregorian calendar was introduced, year was aligned to the seasons and began on 25th of March - the Spring Equinox. It was also the start of the financial year and one of the four days when taxes and rents were due.
However, when Pope Gregory XIII ordered a change from Julian calendar to Gregorian calendar to address imbalance in leap years, UK ignored the Pope's order due to own issues with Catholic Church. Thus, while Europe based on the Gregorian calendar, UK carried on with Julian calendar.
When British finally realised they needed to align with the rest of Europe, they needed to drop 11 days from the calendar to catch up. Treasury was concerned that they would lose tax revenue and moved the beginning of tax year by 11 days to 5th of April.
So why is it the 6th of April a beginning of a tax year? Well, as under Julian calendar 1800 was a leap year and under Gregorian it was not, Treasury noticed they would lose on one more day of revenue income and moved the date to 6th of April.