No, 0161 numbers are not free to call from any UK telephone, even if you are an EE landline or mobile customer. However if you get inclusive minutes to use as part of your monthly contract or pay as you go tariff then you may use these to call 0161 numbers for no extra charge.
So what are 0161 telephone numbers and how much do they cost to call?
0161 phone numbers are local UK numbers which are normally registered private residences and businesses in the Northern England city of Manchester, meaning they cost the same to phone as any other local phone number starting with an 01 or 02 prefix.
Therefore under Ofcom rules, which were most recently legislated in 2015, these numbers are not free to call. However in effect you can call an 0161 number without paying additional money as inclusive minutes that are available on your EE tariff can be used to phone these numbers for free. However if you have run out of minutes you will have to pay an access charge and a per-minute rate, both of which depend on which particular EE pay monthly, pay as you go or landline tariff you are on.