Honestly Honda City 2006 has very good brakes if you compare it with Liana or Corolla. I also faced similar issue once I bought my brand new city 2006 but later the problem was corrected.
Keep on bleeding the brake oil till the time you don’t see new oil coming out from the other end, Ask the mechanic to remove the air from the line during the process. I can bet that previous owner has never performed this exercise.
Always perform this exercise once in every 1.5 years or maximum after every 40,000 km.