accountantpete
OAP
https://www.cyclingweekly.com/video/adjust-bike-gears-142575
It says here that if you are struggling to move the chain from the smallest to largest, you need more cable tension. Is the barrell adjuster the thing on the cables near the brakes?
Yes that will be the cable adjuster. You just need a slight adjustment by the sound of it.
It may be that there is slack and as you are moving the lever you are taking up slack before shifting the mech so tightening up will do. Make a note of how much you turn the adjuster.
If that doesn't work then you may need to check the outer limit screw on the mech to make sure it is allowing the mech to move fully over.