Not quite, you can only phone 013 numbers for no charge if you have inclusive minutes on your O2 tariff. Otherwise you will have to pay the same price as making an equivalent call to any other local UK number.
What are 013 telephone numbers?
013 numbers are a subset of local UK numbers registered to home and business addresses across the country from Eastbourne to Falkirk. They differ from national non-geographic numbers which start with 03 however they cost the same to call for O2 customers.
Cost of calling 013 numbers
O2 customers with minutes remaining in their allowance can use these to phone 013 numbers for free, however if you do not have these minutes you will have to pay a fee determined by the network provider. This consists of a per-call access fee alongside a per-minute rate, thus it is advisable to limit the length of the call as much as possible if you have run out of free minutes.