No, 0370 numbers are charged at the same standard rate as 01, 02 and other 03 phone numbers regardless of which mobile network operator you are with.
However, if O2 have given you inclusive minutes to use on your monthly contract or Pay & Go rewards bundle you can use these instead of paying a charge.
How Ofcom rule changes made 0370 numbers popular
UK government legislation overseen by Ofcom make 0370 numbers more popular as they outlawed the use of the more expensive 0870 numbers for after-sales helplines. This meant companies had to replace these expensive service numbers with cheaper local-rate alternatives, 0370 numbers are ideal for this purpose as only one digit is changed, meaning loyal customers didn’t have to remember a completely different number when making customer service enquiries.