Sellyb does the bike have three chainrings and 8/9or10 at the back? If so you are describing chain-rub caused by cross-chaining.
Let me explain. On a triple it's possible to adjust the front mech to allow the chain to pass through the cage when the chain is on the middle ring, and it can be on any of the cogs (sprockets) on the rear cassette. If however the chain is shifted onto the inner (granny) ring, it only works best on the four or so biggest sprockets. If you shift onto the smallest sprockets the chain "crosses" from near the frame at the front, to away from the frame at the back, and as a result the chain cannot clear the outer plate of the cage and so it rubs.
In your case it sounds like the new cables have stretched through use (they've bedded in if you like) and so the slacker cable no longer holds the front mech so far to the left. This now means that the chain rubs more.
If you bought the bike from a LBS, take it back and ask for your first service. This sort of initial cable adjustment is standard on all new bikes( mine needs doing as well). Otherwise it's the sort of task that if you're brave, you can do yourself.
Look at the front shifter where the cable comes out and you'll see a barrel adjuster:
Shift into the inner ring so that the cable is at its slackest, and simply turn the adjuster as if you are unscrewing it from the shifter, anticlockwise, so that more thread is visible. This puts a bit more tension in the cable. You can feel the cable where it runs to the front mech, and you'll be able to feel it tightening as you turn the adjuster a quarter turn at a time. Aim to take all the slack out of it so that it's taut but not "tight" .
Give that a try and see if it improves things.