I tried the 125 kart race a few times but the AI would always spin me out on the first turn of the first race and I could never recover. I added 7kg 30% to the front, turned my max speed down to 68mph, let the AI overtake me on the first turn so they don't turn homicidal, then made up for it in acceleration. I managed to get gold on the first two races, but I messed up the GT track when I bounced off a curb and spun out. I went back to that race and won it no trouble the next time. I use a DFGT wheel, and it is quite the arm workout twisting around the kart tracks.
Don't forget, if you really hate these races, its super easy to cheat and cut corners at silverstone. You shouldn't need to, but it is really frustrating to do these races a dozen times.