I've filed a total of zero tax forms with the UK government in my lifetime. I've filed several hundred with the US government in a couple of years (and paid third parties money to file "for me" because filing directly is insanely difficult).
Having to do significant tax prep is unusual in the US, too: most US employees have taxes withheld (which is required by law), and usually end up with the Treasury owing them at the end of the year.
Guess it depends on what you mean by significant. Mine is a significant burden, but I'm probably unusual, so I checked the national averages.
The IRS says the average time to complete a tax return is 13 hours:
- 12% complete 1040EZ at 4 hours each,
- 19% complete 1040A at 7 hours each,
- 69% complete 1040 at 16 hours each [1].
Since some 150 million returns will be filed this year [2], that's an aggregate of almost 2 billion hours spent. That's just federal, of course. States are probably less time each, since they piggyback on federal, but there's certainly some time spent there.
Many people fill out the 1040-EZ themselves (a one-page form you can use if you just take the standard deductions and have no unusual tax situations). However, if you can deduct more than the standard deduction, you have non-trivial investments, or any of numerous other situations apply, you have to fill out the full 1040 form, and that requires sufficient effort that there's a substantial tax preparation industry in the US.
That said, there shouldn't be; there's quite a bit of lobbying by the aforementioned tax prep industry to prevent simplification of taxes to the point where everyone could simply file them on their own, as well as to prevent the establishment of an online government-hosted tax prep system. And that's completely ridiculous. The IRS already has more than enough information to simply send everyone a pre-calculated bill.