To secure a garden storage locker you often need an extra-wide yet long shackled padlock to secure the fitting. Many of these lockers will need a padlock that has a shackle up to 50mm wide and 100mm long yet with a diameter not thicker than 15mm. A tough ask but here are some solutions.
As you may need an internal shackle width of 50mm to clear the fitting on your garden locker, you could use something like the U-Lock, normally associated with locking up a bike, as these tend to have a larger shackle loop.
Or you could refashion a bolt to make your own locking mechanism. Drilling a hole in the lower part of the bolt would allow you to use a standard shackled weatherproof padlock such as the Abus 70IB series. If you need to stop the bolt falling through the hole then simply add a metal washer as a collar.