Even though the United Kingdom is an established democracy, the Organization for Security and Co-operation in Europe (OSCE) did observe for instance the 2017 general election. There's both a "needs report" (which did recommend a small mission) as well as final report (both are found on the previously linked page). The mission's scope was rather limited:
In line with ODIHR’s methodology, the EET will not carry out systematic or comprehensive observation of voting, counting, or tabulation on election day. Team members will, however, visit a small number of polling stations across the country to follow election day procedures.
There's also the UK's government response to the reports.
I can't find something similar for the 2014 Scottish referendum though. Was there an OSCE mission observing it?
(The OSCE site is a bit of a mess, so it's possible I missed something or they don't have older stuff on-line.)
I did find a response from the (then) Irish Minister for Foreign Affairs and Trade, Charles Flanagan to a July 2014 Dáil question in which he said
No invitation from the EU or the OSCE to send election observers to monitor the forthcoming Scottish Independence Referendum on 18 September has been received nor is one expected.
It's clear from that that the Irish didn't receive an invitation to monitor the Scottish referendum (via an EU or OSCE mission), but it's a little less clear whether the UK didn't invite the OSCE at all.