Yes! 0808 phone numbers are freephone helplines which are free to call from any UK network, including O2. There used to be a charge from these numbers if you called from a mobile device (but not for landlines) but this was eradicated by a change in Ofcom legislation in July 2015.
0808 numbers and their 0800 counterparts are freephone numbers which means you can call them for free from O2 mobiles, any other mobile network and landline handsets. The company you are calling pays all the costs of the call meaning you don’t have to pay a penny.