Whitbread, which also owns the Premier Inn hotel chain and Beefeater and Brewers Fayre pubs, said trading conditions were flat across the country as household budgets remain under intense pressure, with the exception of London where business is booming.
Costa grew like-for-like sales 3% in the 11 weeks to mid-August as temperatures soared, compared with 8% underlying growth during an exceptionally cold March to May quarter.
Whitbread's underlying sales were up 2.1% during the 11 weeks to mid-August, compared with 3.1% growth in its first quarter. But total sales surged 10.8% as it opened new shops, coffee machines, hotels and restaurants.
Boss Andy Harrison said: "It's clear that the London economy turned a corner some time ago.
"But it's totally unclear to me what's happening outside the M25 and on the evidence I have seen I would say it's flat.
"Wages are rising slower than inflation, particularly energy bills. Outside of London the consumer has less money to spend."
Mr Harrison insisted topsy-turvy weather was to blame for the growth slowdown at Costa, with last summer the wettest on record and this spring the coldest in more than 50 years. Costa's underlying sales in July were flat, a month when temperatures soared.
The coffee chain's underlying sales growth of 5.7% across the 24 weeks to mid-August was also slower than the 7.1% growth seen during the same period a year earlier.
Mr Harrison insisted: "Short-term trading has been distorted by unusual weather. Do not draw any conclusions from 11 weeks of trading."
Total sales at the chain soared 20.8% since the start of March as Costa opened a net 78 new stores in the UK to give it 1,656 outlets. Costa also opened a net 54 new stores abroad, including 30 in China, and now has 2,659 stores in total.
It also added 553 new Costa Express machines, to give it 3,113 of the self-service units.
Costa said it is on track to open a net 300 new stores this year and 850 new machines.
Premier Inn grew like-for-like sales 3% during its second quarter, and were up 2.9% since the start of the year.
Mr Harrison said London was seeing the return of business travellers and foreign tourists, after distortions last year from the Olympics. Total sales in London were up 17.7% since the start of March, and were up 12.1% across the wider hotel chain.
It opened a net 1,270 new rooms in 11 hotels during the period, plus another three restaurants.
Its restaurants saw underlying sales dip 0.1% since the start of March, as its mainly food-based pubs failed to earn a major boost from the heatwave.
Shares in the group dropped 3% in the FTSE 100 Index.
Richard Hunter, head of equities at Hargreaves Lansdown Stockbrokers, said: "The shares have succumbed to some inevitable profit taking, despite the fact that Whitbread's longer-term strategy remains firmly intact."