The Ministry of Defence has told Sky News that although training had begun, it was part of “prudent planning” and may not have to be put into practice.
Plans for the Army and police to be on standby to ensure deliveries do not grind to a halt emerged at the weekend.
As Prime Minister David Cameron oversees contingency plans in case of strikes over the Easter weekend, the Government is already coming under fire for its handling of the situation – after people were advised to stockpile jerry cans of petrol.
Cabinet Office minister Francis Maude has been criticised by Labour after he told Sky News “a bit of extra fuel in a jerry can in the garage is a sensible precaution to take”.
Meanwhile, crisis management expert Paul Charles has said there was “no doubt” contingency planning was also under way by airlines and other large companies who deliver goods around the country on fuel tankers.
“There’s no way this country can last more than about three days with a stoppage. Give it three to four days before you start seeing things grind to a halt,” Mr Charles said.
“That means deliveries of fresh food, it means deliveries of vital goods for car components, things like that.
“That’s why David Cameron will be under pressure, should this strike go ahead, within a three to four-day timeline.”
However, motoring organisations and oil firms have moved to quell concerns, with the AA urging motorists to avoid “turning a rumour into a crisis”.
It says there is plenty of fuel to go around and the situation will only get worse if motorists rush to filling stations and hoard fuel.
AA president Edmund King, said: “If 30 million people suddenly want to fill up 50-litre fuel tanks then you could have a shortage.
“No strikes have yet been announced and there is enough fuel out there as long as people do not fill up unnecessarily.”
The Department for Transport’s own advice to motorists is to “refuel as you normally would”, which has been echoed by Esso.
A spokeswoman for the oil company said: “At this stage no strike dates have been called and the potential remains for a resolution to the matter.”