Sorry to see that these scams have claimed yet another victim. A search of the forums for '£4.50 scam' reveals a large number of these reverse premium rate scams. However usually there are some texts which give you a clue as to who originated the charges.
Ultimately it is GiffGaff's responsibility to explain these charges, as in the absence of any evidence why should you believe that the charges are due to premium rate texts!
The Phone-paid Services Authority is responsible for regulating this sector of the industry and they are very clear:
The network provider is responsible for explaining what the charge on the bill is for and providing the contact information of the service provider.
GiffGaff may try to hide behind section 4.13 of their terms and conditions, which you signed up to when you opened your account. This states:
You may be charged to receive certain premium rate text messaging services and multimedia messaging services. We will not notify you of charges for premium rate services operated by third parties.
Refer them to the regulators unambiguous statement that they are responsible for identifying the orginators of these fraudulent deductions. Then tell them that they can only use Section 4.13 of their terms and conditions to evade responsibility if they can prove that the debits on your account were made in respect of one of the specified services. In practice this means they have to grass on the low-lifes who perpetrate these scams, or refund your money.
Sadly all the mobile phone networks operate a similar scammers charter, where third parties can dip in to your funds without having to prove they have your permission to do so. The network operators take their fair share of the proceeds of these scams, so I suppose it is not surprising that they are somewhat reluctant to assist in bringing them to a stop.
My wife was recently the victim of a similar scam, perpetrated by a company called Remote Games Ltd. I wrote quite a detailed explanation of the steps you can take once you have identified the scammer here:
I hope you manage to get this sorted out.