Because the front master cylinder displaces very little fluid and because brake fluid is hydroscopic (attracts moisture), as the years progress, the fluid looses it's ability to provide what it's supposed to do and that is provide a stable medium to transmit the force applied by the brake lever to the caliper pistons. Add in a tiny amount of air and the braking ability diminishes.
Renewing the fluid, repacing the pads plus careful bleeding the brakes will improve the stopping power greatly. The R3 has excellent brakes, especially the double floating discs, but they must be maintained.
If you refer to the shop manual, I believe you'll find that Triumph recommends changing the fluid every 2 years. That includes a careful bleeding of the system as well.
I use a Mityvac vacuum bleeder and suck the brake fluid from the master cylinder on the handlebar through each bleeder valve on the respective calipers.
70% of the real time braking power are the front brakes.