Marco Pierre White Jr, 21, pleaded guilty to dishonestly making false representations when he appeared at Hammersmith Magistrates' Court.
District Judge Michael Snow told Pierre White Jr he was "not an honest man".
Pierre White Jr is expected to be sentenced at Westminster Magistrates' Court on 8 December.
The Court was told Pierre White Jr asked to borrow his ex-girlfriend's credit card to buy food and requested the card to be unblocked.
The former Celebrity Big Brother housemate, who gave his address as a hotel in Corsham near Bath, then made several unauthorised purchases to the sum of £2,500, including during a visit to an Apple Store.
Prosecutor Robert Chambers said the woman later received an email from her bank about a "high volume of transactions".
When confronted, Pierre White Jr told her he had been accidentally overcharged at a store, the court heard.
He then claimed he needed the card to be unblocked because he had been arrested and needed to pay bail.
The woman accused Pierre White Jr of having a "drug habit" and claimed she had never been in a relationship with him.
But defence barrister Carl Newman said the pair had been in a relationship and she had given Pierre White Jr the card to make purchases in the past.
The judge said Pierre White had been given the card voluntarily but couldn't "suggest he was given permission to go straight to the Apple Store".
The son of celebrity chef Marco Pierre White has admitted dishonestly using his ex-girlfriend's bank card to buy £2,500 worth of goods.