Does the Tax Allowance Benefit Everyone (Regardless of Their Income)?
Not everyone benefits from the tax allowance, but most people with incomes above £11,000 do.  As you suspect, those with income higher than £11,000 only pay tax on their income above £11,000, and thus gain £11,000*tax rate.  However, the personal tax allowance is clawed back at incomes above £100,000 at a 50% rate, so those with incomes above £122,000 don't benefit from the allowance at all.  The official UK government site is here.

At the margin, this means that those with incomes less than £11,000 pay no tax on each additional dollar of income, while those with incomes between £100,000 and £122,000 pay an extra-high amount in tax for each additional dollar earned (the tax allowance doesn't change the tax rate on each additional dollar of income for incomes between £11,000 and £100,000, or above £122,000).  The entire picture is nicely summarized in this Telegraph article.

Here in Canada, we have an equivalent tax allowance, but without the clawback.