On my 2016 Giant Defy with Shimano 105 shifters I am finding it very difficult to reduce the reach on my brake levers and they need pulling almost to the handlebar to brake. Is it possible to reduce the reach by an adjustment in the shifter itself as well as tinkering with the cable at the derailleur end?
I am somewhat confused by your description " they need pulling almost to the handlebar to brake". If you actually need to adjust the bite-point, that is done by tightening the cable at the brake caliper or by adjusting the pistons or using the barrel adjuster.
For mechanical disc brakes with two movable pistons (Defy can apparently have TRP Spyre):
There are 3 mm hex sockets on each side to adjust the the distance of the pistons from the rotor. Each piston is adjusted independently and the sense of rotation to tighten is indicated on the caliper. It is recommended to not using the barrel adjuster for these routine adjustments so as not to limit the available travel of the caliper arm. The barrel adjuster is used to remove the initial slack in the cable.
For caliper rim brakes:
That means that for small adjustments you turn the adjuster. For larger ones you need to unscrew the fixing bolt, tighten the cable and fix it again.
This needs to be done often in order to compensate for the brake pads getting worn. Small adjustments using the barrel adjuster, larger ones by unfixing and re-fixing the cable.
Do not forget to always close the small (often plastic) quick release lever. That can be a possible source of a similar problem. See https://thecyclemechanic.co.uk/knowledge-hub/using-quick-release-brakes/
Tutorials are also available:
The lever reach should be adjusted at the shifter, not at the brake caliper. It controls the depressed angle, the distance of the lever from the handlebar when the lever is released.
There is a screw in the shifter. Take off the hood to adjust it using a 2 mm hex key.
There are tutorials available:
For hydraulic disc brakes: the pistons are adjusted automatically. One can only adjust the lever, not the brake caliper.