Assuming you have only the basic personal tax allowance, and you pay NI contributions at the standard Class 1 (employed person�s) rate, the figures are as follows:
INCOME TAX
Your personal allowance this year is �6,035. (The current allowance of �5,435 is being increased retrospectively to cover the whole year).
On �13,000 you will pay 20% on �6,965 = �1,393 = 10.7%
On �27,000 you will pay 20% on �20,965 = �4,193 = 15.5%
NATIONAL INSURANCE
You will pay 11% on all earnings above the primary threshold which is �5,435. (This figure is not being increased in the same way as the Income Tax allowances).
On �13,000 you will pay 11% on �7,565 = �832 = 6.4%
On �27,000 you will pay 11% on �21,565 = �2,372 = 8.8%
Your total deductions on a salary of �13,000 will therefore be �2,225 (17.1%)
On a salary of �27,000 they will be �6,865 (24.3%)