Our users are primarily in the UK.
We already have the sites hosted on a sever in the UK.
Would there be any latency benefits in having the DNS name servers located in the UK as well?
Short Answer: Minuscule benefit, if you have big enough TTL.
Long Answer: To understand it, you need to understand how DNS works and terms like DNS caching, TTL (time to live).
On very basic level, DNS converts domain name to an IP address. While setting A-record (or other records), we also set TTL (time to live) which is the caching duration for the Domain-IP mapping at various ISPs around the web.
Now, let's say, you have your DNS server in US. When the very first user fetches your website from UK, the ISP in UK will have to go to DNS server in US to find out your IP and then it will cache it for say 24hrs (if your TTL is 24hrs). All other users, will be directed to your IP based on this entry for next 24hrs. After 24hrs, the same cycle continues.
So, it basically depends on your TTL. If your TTL is very small (say 1 min), then it may cause a latency for atleast 1 user every minute. If TTL is 24hrs, then latency would be only for 1 user per 24hrs.
Note: I have taken a simplistic view of DNS to explain it.