Low Voltage Wiring Code

Probably. This is an international forum. Where are you?

California.

EVERYTHING's illegal in kalifornica

So long as you don't terminate the 24VDC wiring onto a receptacle of a type normally used for mains power then it should be fine.

Segregation of services should also be considered, eg don't run these in the same duct as the mains wiring.

I have deliberately avoided the use of the term "low voltage" per the OP's definition. We call that extra low voltage. Low voltage(<1000V) is what comes out of your power socket, still potentially lethal but low.

I did the same thing in Texas. I just don't let them in my garage!!!

If the conductors are protected from overcurrent, either by fuses or by being Class 2 low-energy circuits, they can be run inside walls just like Romex cable for 120-volt wiring. The objective is to prevent shock or fire.

Unless stated differently in your local code, you would only need conduit for physical protection of the cable.

If protection of the cable is not an issue, your installation should be good to go.

be it in the USA or UK, why go to all the trouble of hiding the cable as its in the garage, just surface run plastic conduit with the cable inside, use a suitable outlet, but MARK the outlet 24Volts, or even betterv as it sounds you are moving the timer location, put the timer near the the outlet.. just an idea!

I don't think that he mentioned an outlet from the transformer. I believe that he means a plug-in female end that is made onto a power adapter cord.

Yes, the NEC does cover you power adapter cable as a "flexible cord."

Technically speaking, the cable is not likely to be rated for running inside a wall, but it would be OK to conceal it inside a wire duct or a piece of conduit.

NEC References:

400.7 Uses Permitted.
(A) Uses. Flexible cords and cables shall be used only for the following:
(8) Appliances where the fastening means and mechanical connections are specifically designed to permit ready removal for maintenance and repair, and the appliance is intended or identified for flexible cord connection

400.8 Uses Not Permitted.
Unless specifically permitted in 400.7, flexible cords and cables shall not be used for the following:
(5) Where concealed by walls, floors, or ceilings or located above suspended or dropped ceilings

Just like your door bell wiring, the low voltage cable can be ran along and through the walls. However you mentioned that you plugged in the transformer below the work bench. I assume that this is a 120 volt primary and a 24 volt secondary. The 120 volt "plug/wire" connections must be inside a gang box for code and for your protection.

We don't want to see you sitting at your work bench, cross your legs on a nice summer day and have your toe hit the line voltage connection.

Go to your local county web site and pull up the codes for this type of installation or call your local electrician just to be sure you are properly adhering to the code.

If it wasn't legal, then there's a lot of thermostat and doorbell wiring that has to be ripped out in the USA!!

Thermostat and doorbell cables have a non-metallic sheathing that encases the individually insulated conductors. Power cord for a low power appliance like a blender or lamp does not.