I haven't made a claim for this myself, but the only benefit for travel costs is for a parent accompanying a child who is in hospital. Even then, it's limited to public transport, taxi, hackney or car parking charges and the benefit isn't available on all plans.
You can give it a shot, but I don't think they'll pay anything out. For one, it's not a benefit listed in their documentation, and with medical costs as they are, insurers are probably sticking rigidly to that. Even if they wanted to offer some cover, they have no way of verifying that the fuel purchased was for the purpose of the out-patient visits, and have no way of knowing how much fuel is needed for the trip from home to the hospital.