It's hard to see how the British Base (Rothera) could have helped. There is absolutely no Avgas kept on base as BAS operate twin otters and a dash 7.
The only petrol is for use in Skidoos and honda generators used by field parties. This fuel is carefully budgeted for, at least a season in advance and there isn't a great deal of slack in the system. There aren't vast quantities of drummed petrol just lying around waiting to be "sold". And how much would they have to charge - try and imagine to true economic cost per litre of a drum of fuel two or three depots down the line. By the time it has been delivered to Depot X, the Twotter may have used 10 drums of Avtur. I would think that the situation at McMurdo is similar.
AFAIK Polly Vacher had fuel paid for and depoted for her trip, it wasn't "Base" fuel.
I have worked in the Antarctic for nearly 20 years but I don't know what the British policy is on "adventurers". I think it is done on a case by case basis. There is no blanket ban on entering the base such as that in force at South Pole Station (an American base) They always get a warm welcome on base, in my experience and help if required (but don't tell anyone...). Fuel (Avtur) may be supplied to other nation's aircraft but it is usually on a mutual back scratching arrangement.
FBF