I think that you'll be out of luck.
Several energy suppliers used to offer 'low user' tariffs that charged slightly higher than usual per unit of gas (or electricity) but without a standing charge, so that very light users of energy (or, say, people who only used their holiday homes occasionally) paid lower bills.
However OfGem ruled against them and demanded fewer tariffs, with everyone having to pay for their electricity/gas connection through a standing charge. So the energy companies were forced to abandon their 'low user' tariffs and obliged to charge everyone the standing charge.
For example, I used to pay only around £30 per year for my limited use of gas (with British Gas) but OfGem's ruling has put that up to around £100 per year, with British Gas having no say in the matter.