There are pros and cons to making the switch:
Pros:
A shorter URL is generally better for link building, SEO, and social sharing
Customers may assume your site is brandname.co.uk and type that directly into their browser (they probably won't guess that they should add "shop" at the end)
The URL would be easier to remember
The brand URL might look more trustworthy and help with click-through-rate and conversions
Cons:
You will lose a little link authority by using a 301 redirect to the new site (a 301 redirect will pass a majority of your link authority to the new domain)
You will lose some trust by switching to a new domain that hasn't been around for years but you can make this up over time and by earning high quality links