Whitbread's chief executive Andy Harrison said he acknowledged that "Starbucks has issues", and added: "UK consumers are voting with their taste buds."
While Starbucks UK last week promised to pay around £20m in corporation tax over the next two years, the ongoing row sparked customer boycotts and protests.
Guardian Stockbrokers' Atif Latif said there was no doubt the tax row had benefited Costa.
"This uptick at Costa is as a result of clever promotions, a large increase in Costa outlets and greater pricing parity now that many new customers have switched to Pret a Manger and Costa from Starbucks given the news on tax," he said.
"If Costa can capture and retain these customers then we envisage that many will not move back to Starbucks as they are more concerned about the ethical nature of businesses, which remains a priority over taste or habits."
Whitbread, which also owns Premier Inn and the Beefeater and Brewers Fayre pub chains, said total sales across the group were up 14.4% as its brands continued to outperform the market.
Its Premier Inn advertising campaign - featuring comedian Lenny Henry - boosted like-for-like sales at the hotel chain by 2.5%.
But growth across the group slowed when compared to its first half, which was boosted by the UK's wet weather and Olympic Games.
"Whitbread continued its strong growth momentum with total sales up 14.4% together with good like for like sales growth of 3.3%. This once again demonstrates the strength of our brands," Mr Harrison said.
"The economic environment remains challenging with no change in our background consumer market. We are on track to deliver full year results in line with expectations."
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