No, standard UK local call rates apply to 01 numbers meaning they are not free to call from an O2 mobile phone, or indeed any other telecoms network as ruled by Ofcom (effective 1st June 2015).
Despite this, free inclusive minutes offered as part of your Pay Monthly or Pay & Go deal can be used instead of the standard charges.
Standard call charges for 01 numbers
01, 02 and 03 numbers are charged at an identical rate from O2 mobile phones in compliance with the law, this includes an access charge alongside a per-minute fee which may change depending on whether you are calling on a weekend or in the evening.
Using your O2 inclusive minutes to call 01 numbers
Many O2 contract and pay as you go tariffs contain an inclusive minutes allowance which can be used to call local numbers, including 01 numbers, for no additional charge – the only thing that will be used up are your minutes so remember to check before you call in case you are running low.