LONDON, Nov 29 (Reuters) - Britain's antitrust regulator said it would launch a review of loyalty scheme pricing by supermarkets, such as Tesco's Clubcard and Sainsbury's Nectar, considering its impact on consumers and competition in the groceries sector.

Loyalty schemes have proved hugely successful for supermarkets, with retailers offering much lower pricing for members on a growing number of products.

Reviewing the whole sector, the Competition and Markets Authority (CMA) also said on Wednesday that it had found some branded suppliers had pushed up prices by more than their costs increased, but in most cases, shoppers could find cheaper alternatives.

It did find one area of concern, however, with the CMA saying ineffective competition in the baby formula market could be leading to parents paying higher prices.

The CMA had examined whether weak or ineffective competition among suppliers and producers, or in specific product categories, could be contributing to price inflation.

It ruled in July that Britain's high food price inflation had not been driven by weak competition among supermarkets.

It looked at 10 product categories - baby formula, baked beans, bread, chilled desserts, lemonade, mayonnaise, milk, pet food, poultry and ready meals.

UK food price inflation reached its highest since 1977 in March at more than 19%, according to official data. By October it had slowed to 10.1%, but is still a major strain on the finances of many households. (Reporting by James Davey; Editing by Kate Holton)