The only real difference in SEO terms will be with local or geo-location based searches. They will always favour local factors - like country specific domains and servers/IP ranges in the same continent. So unless you're specifically targeting those, it doesn't matter. Especially as tools like Google Search Console will let you pick which country you're looking to target in search results.
However, from my experience and some of the UX studies that I've read, it seems that people's perceptions are also a factor with TLDs. People in the UK will be more familiar and more trusting of .co.uk (or the more recent .uk) domains as they're more used to seeing them. They get the UK versions of all the big sites they use - Google, Amazon, eBay, Facebook, etc... so it's sort of a subliminal expectation. If they see a list of similar sites on a page of search results, a portion of them will be drawn to the .uk options (and vice-versa for other countries and their relevant TLDs).
TL;DR - I'd go with the .co.uk