The two accused — a sergeant and a private in the Mercian Battle Group — have been arrested by military police for allegedly encouraging a boy and a girl to touch them through their clothing

They are said to have filmed the children before showing the footage to shocked comrades on laptops. They were held following complaints from other servicemen.

PM David Cameron was informed of the allegations by defence chiefs and was said to be “deeply shocked”.

The Afghan government says it is “disgusted” and has demanded an immediate investigation into the case.

It is the first time allegations of abusing children have been levelled against British troops in either Iraq or Afghanistan.

A source close to the probe said last night told the Sun: “Nothing has been proved. What we have to establish is whether we are looking at sexual predatory behaviour or totally ill-judged larking about.

A senior defence source added: “We are determined to get to the bottom of this ASAP. Any criminal behaviour will be dealt with robustly and must not be allowed to undermine the excellent work our armed forces are doing in Afghanistan.”

The allegations come a little more than a week after the US military was rocked by a video in which Marines apparently urinated on Taliban corpses.

Britain has about 9,500 troops in Afghanistan, mainly based in Helmand where they are battling a Taliban insurgency.