Property experts ESPC said single-bedroom flats in Polwarth, Shandon and Tollcross have increased by 22.3 per cent over the last three months.
Average selling prices in these areas were £200,965 between February and April 2018, compared with £164,285 for the same period last year.
Similarly, one-bedroom flats in Dalry and Gorgie increased by 19.9 per cent to £143,162 over the last three months, compared with £119,442 during the same period last year.
ESPC said high demand meant flats were selling quickly and for well over valuation figures.
David Alexander, of city estate agents DJ Alexander, said one explanation for the surge in demand was the effect of the Land and Buildings Transaction Tax (LBTT) which replaced stamp duty three years ago, with higher rates on the most expensive properties and lower rates for those at the bottom end.
He said: “We’re seeing a large flow of money into smaller flats from people buying them as buy-to-let.”
Investors with more than one property must all pay the three per cent second homes supplement, but they could pay very different amounts of LBTT depending on the house price.
Mr Alexander said: “If you had someone who was thinking of spending £1m to buy a property in Heriot Row he would immediately face LBTT of £78,000 and if he already has another property he will also have to pay an extra £30,000, so that’s £108,000 in tax.
“But if he decided instead to buy five one-bedroom flats at £200,000 the LBTT would total £5500. You would still have to pay the extra £30,000, but that would mean the total tax was £35,500 instead of £108,000.
“And with the smaller properties you also have the benefit of the value being more likely to rise.
“If you asked me whether a £200,000 property could rise by 10 per cent I would say yes, but if you asked me the same about a £1m property I’d say there was very little chance.”
He said as well as the buy-to-let purchasers there were also investors buying smaller flats to rent out on AirBnB.
“People buying a flat and letting it out on AirBnB is having an effect on the market too. It’s an attractive proposition - you’re paying very little LBTT, it’s an unregulated market and you can let it out for good prices.”
ESPC said a shortage of property was continuing to drive up prices in the Capital.
The number of new homes brought to market between February and April decreased by 8.3 per cent from last year. The number of homes sold across east central Scotland was down by 6.6 per cent. And the average selling price increased by 7.8 per cent to £234,864. ESPC business analyst Maria Botha-Lopez said: “The market is strong, and demand is there, so this could be a good time for those who are thinking of selling their homes to do so.”