Britain's biggest supermarket, Tesco, is facing two official investigations over claims that it deliberately advertised cut-price alcohol as "bait" to lure bargain-hunters.

Trading standards officers have launched an investigation into whether Tesco broke new laws by running special offers while failing to ensure it had enough stock to meet demand.

In a separate move, the Advertising Standards Authority (ASA) is looking into whether Tesco broke advertising rules in the way that it promoted the offers and refused to remove banners at front of stores despite not having the stock to sell.

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The investigations are the latest moves as retailers come under increasing scrutiny for the way that they bend guidelines designed to ensure that the public are not misled by bogus sales and money-off deals. The consumer group Which? recently completed a three-month investigation during which it found several examples of misleading deals from retailers. Among several misleading cases, Which? found:

*Waitrose blueberries were on "half-price" for six weeks after two weeks at the "higher price". Goods should be sold at the higher price for at least 28 days, government guidelines say;

*Marks & Spencer had "half-price" cherries at £2.49 when the higher price was only 50p more;

*Sainsbury's sold Jacob's Creek chardonnay for £4.79 for months after offering its higher price of £6.79 for just two weeks.

Under the Unfair Consumer Practice Directive, which came into force in May last year, retailers are forbidden from advertising goods for which they can expect they have insufficient stock – a practice known as "bait advertising".

The allegations against Tesco were made by Rosie Cooper, a Labour MP, who contacted trading standards and the ASA after visiting a branch of the store in Liverpool. She said she tried to buy a one-litre bottle of Baileys which had been advertised for sale at £8. But the West Lancashire MP found the offer was "out of stock". She then tried a further two stores which were also out of stock. She said: "When I contacted Tesco's head office their customer services department told me 'all stores should get some stock, but not a lot, granted'." She did not say that she was an MP.

"So I told them I was contacting trading standards and they still said they would not act which I find absolutely amazing." Ms Cooper, who said other shoppers had made complaints about the non-availability of special offers in Tesco, said Tesco had refused to remove the misleading advertising from the front of its stores.

"On a personal level, it doesn't matter but on a national level I think Tesco is getting too big for its boots. If they have been using bait advertising and think they can get away with it then somebody should stop it."

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Tesco denied that it had deliberately understocked the offer in question. "The response from our customer service centre to Ms Cooper was wrong," a spokesman said.

"There was plenty of stock ordered to ensure enough of these products for all customers across the country and we apologise that she was not given an adequate explanation.

"As you would expect in the run-up to Christmas, these promotions were extremely popular with customers. Additional supplies were ordered in as quickly as possible." Tesco said it was addressing another complaint from the MP – namely, that Jacob's Creek wine was on offer advertised for £3 but was being sold for £6.

Liverpool Trading Standards Office confirmed it was looking into a complaint and said that any company found to be in breach of regulations on bait advertising "could face a substantial fine or be at risk of prosecution".

An ASA spokeswoman said: "We do get these kind of complaints on a very small but regular basis. People feel very put out if they have gone to a store for a particular offer and it has not been available."

The ASA investigated and rejected two complaints against Tesco last year for allegedly running promotions which were not fully supported.

Jeff Bray, who is a lecturer in retail consumer behaviour at Bournemouth University, said retailers sometimes understocked special offers, especially for "big ticket" items at electrical and furnishings stores, in order to create a buzz and ensure customers flock through the doors. Supermarkets would find that such tactics rarely worked, however, because the items would rarely offer enough money off and could irritate customers.

He added: "There are a number of questionable ethics in some of the offers retailers are exposing us to. The first and obvious one is that there are quite loose laws on money-off deals and some retailers are exploiting those rules by putting up the price of goods for a limited time before making a discount.

"There are other slightly less obvious tricks like putting coloured bands on a product saying 10 per cent off where the band is much bigger than the extra amount in the pack meaning that, cognitively, the consumer is being misled."

He added: "The law is very loosely regulated in this country compared to others and retailers as are looking to exploit every opportunity."