In the U.K. If you are employed, your tax is worked out for your through the Pay as You Earn system. If you are self employed you fill in the rather good self-assessment form online and your tax is calculated for you.
I did it for years with no need for an accountant, despite my business was complicated by special circumstances (non-UK customers, tax-exempt research funds, etc).
The one year I was in credit, they wired me the money within days.