Fuel Issue

Hi all

I have a Triumph trophy 1200 2003.

Developed a running issue and I am confident it's a fuel issue rather than electrical.

Starts fine and idles really well, around 2000 and 3000 rpm it's seems to hesitate and run as if its missing, after 3k it feels as if it is running better but still with a slight stutter. When we and my girlfriend were out on it yesterday it came to a stop as if it had run out of fuel but the gauge wasn't on the red. I put the tap to reserve and after a little time it started and ran wonderfully. Straight to petrol station and filled the tank. Fault still present. I am thinking carb service kit but these don't seem to be readily available. I have read a few threads about hoses cracking but I don't have a fuel leak. Any help would be muchly appreciated.
Many thanks