The Finn topped the times on Wednesday by 0.4s and declared himself satisfied with the way the car handled on both days.
“I think weve made a small step forward,” he told reporters at Silverstone.
“Looking at the runs, I was consistently able to set very competitive times; it wasnt just one run that we did just to get a time. That is quite encouraging.
“But still I am sure it will be very close in qualifying and the race like its always been.
“We need to carry on pushing and hope it pays off.
“We had a small modification to the brake ducts which felt like it was a positive step, and another few small modifications to the aero today – no big things, but they do feel like an improvement, so thats always a very positive sign.”
Ferrari beat McLaren at last year's British Grand Prix, but Kovalainen doesnt think that means the Maranello squad starts as favourite this time.
“Weve seen that the last years results dont necessarily mean that much,” he said.
“I think where Ferrari were weak last year theyve been strong this year, and vice versa.
“I feel that we have a very competitive car in the high-speed corners.
“Earlier this year we were losing a bit of time in slower corners, like the last sector in Barcelona and the last sector in Turkey, but weve been working hard to improve that.”
And while Ferrari also dominated last weekends French Grand Prix, Kovalainen reckons McLarens potential was masked by the penalties that left both its cars starting from the midfield and spending most of the race in traffic.
“Ferrari had a great pace in Magny-Cours, but on the other hand I dont think we were able to show our true pace there,” he said.
“Certainly with the car I had in the race, I felt that there was a lot more to come had I been able to start higher up on the grid and been in the clean air for more time.”