Technically 0113 numbers are not free to call on O2, however if you get inclusive minutes as part of your rewards bundle or monthly contract stipulation you can use these instead of paying the financial charges.
Background on 0113 numbers
The 0113 telephone area code is registered by default to personal and business lines in the UK city of Leeds. However it is possible to register these numbers from outside their usual Leeds area so be cautious if you have been called by an unknown number.
Cost of calling 0113 numbers from an O2 mobile
Normally O2 customers will have to pay an access charge of 30p for SIM Pay & Go customers or 35p for monthly contract users to connect a call to an 0113 number, followed by an equivalent per-minute rate. However you can avoid these payments if you get inclusive minutes as part of your rewards bundle or contract allowance, all that will be affected is your minutes balance.