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Since it is hardy to -17 degrees C (0 degrees F), and Liverpool experiences mild winters, I would go ahead and give it a whirl. It will need a large pot, though, as they grow fast. You may only want to keep it in a pot for a couple of years, then rehome it where there is more room in the ground. You can always trim it back when it starts getting too large for your pot or even root prune. If you see a particularly cold snap coming up, i.e., below freezing weather, some winter protection would see it through.

https://plants.ces.ncsu.edu/plants/berberis-darwinii/

https://www.gardeningknowhow.com/ornamental/shrubs/barberry/barberry-shrub-care-tips.htm

Here's an article with tips on how to care for it:
https://www.gardeningknowhow.com/ornamental/shrubs/barberry/barberry-shrub-care-tips.htm
The best time for pruning is after the bush has flowered in the spring, but cutting away dead and damaged branches should be done now.

In order to be fair and include gardening information for everyone, it is also necessary to provide information on any plants of interest. All plants have the capability to become invasive given the proper environment, yet all plants are not invasive everywhere.

It would be unfair to those that live in an area (such as mine) where these shrubs are not invasive to not include information for those who wish to grow them.

It is up to each individual to garden, responsibly, and research what is sustainable in the area. Should the answer not present itself clearly, then one can contact local extension services. The local extension services in an area will be able to tell you what plants are blacklisted in an area, or what may grow well in your area.

Here is a link to help you find the closest extension service to you, so that you may request information about plants before you plant them in your area:

https://www.gardeningknowhow.com/extension-search

Contacting them before planting will help prevent you from planting any other invasive species in your area, again.

Barberry shrubs or hollies could work well. The Oregon publication lists pyracantha as a deer resistant shrub. However, deer will eat about anything if they are hungry enough.

https://www.gardeningknowhow.com/ornamental/shrubs/shgen/using-defensive-shrubs.htm

https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-8/zone-8-deer-resistant-plants.htm

https://extension.oregonstate.edu/gardening/techniques/deer-resistant-plants-central-oregon

They need at least part sun and won't do well in the shade. Here are some shade plants that may work:

https://www.gardeningknowhow.com/ornamental/shrubs/shgen/shade-loving-shrubs.htm

https://www.gardeningknowhow.com/special/shade/evergreens-for-shade.htm

There are lots of prickly plants that could discourage cats. Shrub roses or barberry come to mind. Barberry comes in a variety of sizes, shapes, and colors.
Here is more:

https://www.gardeningknowhow.com/ornamental/shrubs/shgen/using-defensive-shrubs.htm