The inquiry centres on the company’s alleged failure to make clear that by signing up to the service customers are often agreeing to pay not just for one ringtone but for a regular, indefinite service.

Parents have complained that the small print explaining how the service works is so dense that children do not understand that they are entering into a long-term — and expensive — contract.

Many say that they have discovered the truth only when they examine their child’s soaring mobile phone bill.

The Crazy Frog tune was so successful that it recently beat the rock band Coldplay to No 1 in the pop charts.

At £3 a go, just four of the novelty ringtones is equivalent to the cost of an entire Coldplay album. Icstis, the body that oversees premium-rate numbers, is now investigating whether mBlox, which provides the premium-rate numbers to Jamster, the “face” of the ringtones, is in breach of the industry’s code of practice.

The regulator, which has received more than 100 complaints about the hit service, is examining the company’s terms and conditions to discover whether they really are too opaque for consumers, particularly children, to understand. The regulator is also looking at whether the service deliberately seeks to advertise and promote ringtones to the under-16s — those least likely to realise the contract into which they are entering.

If it is found to be in breach of Icstis’s code, mBlox could face a fine of up to £100,000. It could also be barred from operating. Though Jamster, Britain’s biggest-selling ringtone company, could technically source the premium-rate numbers it uses elsewhere, the move could force it to change its sales methods.

Rob Andrews, an IT consultant from Nottinghamshire, told of his alarm at finding that his daughter Alicia had racked up a bill of nearly £70 in only a few months.

He discovered from Orange, the network operator, that she had subscribed to Jamster, which had sent ringtones and texts every couple of days to her phone, each costing at least £1.50.

Alicia was adamant that she had never signed up to a subscription service and Mr Andrews believes that she must have subscribed without realising it. Internet sites are awash with similar complaints.

The Crazy Frog ringtone, spawned seven years ago by a Swedish motorcycle enthusiast, is based on the sound of a revving moped.

It is the first ringtone to enter the pop charts, where it stayed in the No 1 slot for four weeks.

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