Yes, there is a minimum amount you need to earn. However, it has nothing to do with whether you are married or have dependents or anything... each person is given a Personal Allowance each year and the amount they can earn before paying tax is determined by their tax code.
The personal allowance is based on your age and your total income. There are 3 levels of personal allowance: Basic, Age 65-74 and Age 75 and over.
Most people will have the Basic personal allowance, which for the 2012/2013 tax year is £8,100 (tax code 810L), with an income limit of £100,000 (i.e. if you earn more than £100,000 you get less allowance). So, if you earn less than £8,100 in this tax year, you don't have to pay any tax, but if you earn more, then you pay tax on anything you earn above £8,100.
For people aged 65-74, the personal allowance is currently £10,500 and for Over 75 it's £10,660, both with income limit of £25,400.
If you end up paying too much tax, for example if you only work for part of the year and pay tax during that time, but overall your total income is less than the personal allowance, then you can claim a tax refund within a certain time limit.
See here for more info:
http://www.hmrc.gov.uk/incometax/codes-basics.htmand:
http://www.hmrc.gov.uk/incometax/personal-allow.htm