Will this fourth round of sanctions have the desired effect of slowing Iran's nuclear aspirations?
Last month, the UN Security Council voted to impose a fourth round of sanctions on Tehran for failing to halt its nuclear enrichment programme.
A spokesman for the UK's Civil Aviation Authority told the BBC any move to withhold fuel would be down to individual fuel companies.
New US sanctions were signed into law by President Barack Obama last week.
The US sanctions prohibit the sale or provision to Iran of refined petroleum products worth more than $5m (£3.3m) over a year. Paul Reynolds, world affairs correspondent for the BBC News website, said it might be that fuel companies are worried that their sales over a year might add up to $5m, in which case they could face a possible ban on doing business in the US.
An Iranian aviation official said Iranian airliners were filling up with as much fuel as possible inside Iran. But they were also having to refuel in countries along their route not imposing a ban, a move which the official said was doubling costs.
"Since last week, our planes have been refused fuel at airports in Britain, Germany and UAE because of the sanctions imposed by America," Mehdi Aliyari, secretary of the Iranian Airlines Union, told Iranian media.
He said the national carrier Iran Air and a private airline, Mahan Air, had both run into refuelling problems.
Iranian lawmaker Heshmatollah Falahatpisheh said Iran would retaliate.