Have you inspected the front discs, pads, fluid and any history?
To check there is no air in the brake lines or problem with the master cylinder. Engine off, pump the brake pedal several times, the pedal should firm up with MUCH less travel. ie. cannot push it down to the floor.
If there was an issue with the brakes, you would hope it would have been flagged up in last MoT?
fwiw, the brake pedal on my 57 Jazz is not as 'sensitive' as my new car. I have to push the pedal further to slow down. It's been like that even after fitting new discs, pads in 2021. Brake fluid changed every 2-3 years. Only done 21k miles, owned from new.
If in any doubt, recommend you get a second opinion from a garage.