You are able to withdraw money from an ISA however this does not change the amount that you are able to deposit for that tax year.
For example: if you deposit £20,000 in a Cash ISA during the tax year, but then take out £1,000, you cannot then add another £1,000 in the current tax year.
Additionally there may be interest penalties if you wish to withdraw your money from a Fixed Rate ISA product or stocks and shares ISA.