LONDON (Reuters) - The number of British shoppers hitting the post-Christmas sales dipped by 4.2 percent year-on-year on Wednesday, offering no relief for struggling stores that had already discounted heavily to encourage spending in the run-up to the holiday.

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Out-of-town stores and shopping centres were hit harder than towns and cities, but visits to both fell for the third year in a row, according to data for the first hours of trading on the morning after Christmas.

Shopping centre visits were down 6.7 percent by midday, market research firm Springboard said, while traditional town and city shopping streets saw a 2.8 percent drop.

Britain’s retailers had been hoping Christmas would revive spending after a bleak year for much of the sector that has seen a string of chains go out of business or announce shop closures.

The sector has faced uncertainty over Britain’s exit from the European Union, rising labour costs and higher business property taxes as well as unseasonably warm weather.

Stores were pinning hopes on a surge in shoppers seeking bargains to counter poor trading in November and early December.

Clothing chains such as Primark ABF.L, Superdry SDRY.L and online retailer ASOS ASOS.L warned of weak sales earlier in December, after what Sports Direct SPD.L owner Mike Ashley said was "the worst November in living memory" for retailers.

Springboard said one reason for the drop in footfall was the almost continuous discounting, particularly since November’s Black Friday.

“However, many retailers offer greater discounts online than in store, which discourages shoppers to visit retail destinations and bricks and mortar stores,” Springboard said.

Springboard said many people were eating and drinking as well as visiting shops, a trend that was benefiting high streets, where there were more restaurants and other venues, more than retail parks.

London’s Oxford Street, Regent Street and Bond Street saw a 15 percent increase in footfall year-on-year by 10.30 on Wednesday, the New West End Company said, and it forecast 50 million pounds would be spent in the district by the end of the day.

“International tourists are out in force driven by the weaker pound, as well as domestic shoppers who are looking for a day out after family celebrations yesterday,” said chief executive Jace Tyrrell.