You cannot phone 0121 numbers for free on O2 or any other mobile network unless you have inclusive minutes on your Pay & Go rewards bundle or contracted allowance.
Background on the Birmingham (0121) area code
All new telephone landlines registered in the UK city of Birmingham are designated an 0121 area code prefix by default, meaning it is easy to trace the origin of calls from these numbers. There may be exceptions to this though as you can register 0121 numbers outside the normal area of the UK’s second largest city.
Cost of calling 0121 telephone numbers on O2
If O2 has given you inclusive minutes to use on either your Pay & Go rewards or monthly contract allowance then you can use these to call 0121 phone numbers instead of paying a financial fee. Otherwise you will have to pay an access charge of either 45p (Pay & Go) or 55p (monthly contract) alongside a per-minute fee.