Not at all. There is no explicit permission to do so, as you would very quickly find out if you have already filled your ISA by 31st March and pay into it again between 1st and 4th April.
In practice, the only reason people can consider the tax year as ending on 31st March is because most people have no significant taxable events occurring between then and 5th April.
But if you sell shares that put you over the capital gains threshold, receive dividends, pay into your ISA or even receive interest from your bank account in those few days, these are all considered taxable events. For most people they are a non-issue due to the tax-free allowances on all these classes of income, but if you exceed the tax-free allowance for any of them, it's important you apportion them to the correct year.
In practice, the only reason people can consider the tax year as ending on 31st March is because most people have no significant taxable events occurring between then and 5th April.
But if you sell shares that put you over the capital gains threshold, receive dividends, pay into your ISA or even receive interest from your bank account in those few days, these are all considered taxable events. For most people they are a non-issue due to the tax-free allowances on all these classes of income, but if you exceed the tax-free allowance for any of them, it's important you apportion them to the correct year.