And the jewellery group Signet - which includes H Samuel and Ernest Jones - said its sales were so strong it expect profits to be higher than predicted.
The news will allay fears of a crash in High Street spending, which could be bad for the UK economy.
"
This performance demonstrates the strength of our business in what has been a competitive trading environment
"
Vittorio Radice, chief executive Selfridges
On Tuesday two stores - Dixons and Laura Ashley - said trading had been disappointing and warned that their profits would be hit.
The picture of the High Street that is emerging from Christmas trading statements is one of winners and losers, according to Robert Clark, research director of the Retail Knowledge Bank.
"We are seeing a slowdown in spending growth and it's long been expected," he said.
Tough competition
Selfridges said that its sales in the seven weeks leading up to Christmas were reasonable and its winter sale had started well.
Sales in stores that were open at the same time last year increased by 7% in the six months to 4 January.
Sales for the six week Christmas period were up 2%.
"This performance demonstrates the strength of our business in what has been a competitive trading environment," said chief executive Vittorio Radice.
He admitted that Selfridges was not immune to a spending slowdown but said he thought the stores would be comparatively resilient.
Sparkling sales
House of Fraser said it had put in a creditable performance against a background of a weaker general retail environment.
The company said its comparable sales grew by 1.6% in the 23 weeks to 4 January.
Signet said that in the eight weeks to Christmas its comparable sales in the UK increased by 3%.
Ernest Jones put in the strongest performance and diamond sales increased substantially at both Ernest Jones and H Samuel.
The chief executive Terry Burman described it as a relatively robust performance.
In the US, where Signet's stores include Kay Jewelers, sales were also strong.
The US side of the business makes up 71% of the business.
But the company said the weakness of the US dollar would dent profits from the US operations.
Supermarket strength
Safeway was the first supermarket to give details of its Christmas trading.
Its sales in the four weeks to 4 January grew 4.2% making it the company's best Christmas.
Safeway also announced that it was being taken over by its smaller rival, Morrisons.