You should be given a proprotion of the threshold each month/week, unless this is a 2nd job and you are using your basic rate allocaton elsewhere. In this case, you may be issued with a D0 tax code, meaning "tax everything at 40%". By month 12 of the tax year, you should have had all of your basic rate band, unless you have a non-cumulative tax code (week/month 1) .If this is a new job and you weren't working before in the tax year, you may not get the unused basic rate band from previous months until you are allocated a tax code by HMRC.
Are you saying you earned �5000 gross and paid �2000 tax on it? What is your tax code?