As a result I'm interested in implementing a system to measure
employee engagement in the workplace to pick up on common trends. How
would I go about doing this?
As they say "You can learn a lot by asking".
Here, I'd worry that you feel the need for a "system", rather than just walking around and talking to people. Systems like Survey Monkey and such are a poor substitute for speaking with people directly, listening to what they are actually saying and watching how they are acting.
A system typically abstracts what is really going on and attempts to cram it into a number. That way (or so the theory goes) you can track the number over time, and see if it is getting "better".
But "engagement", "happiness" and "feeling valued" don't work that way (at least not in my opinion). And any number you use to represent them is a poor substitute. Attempting to measure engagement as a number may result in people feeling more alienated ("I'm just a number - they don't even want to talk to me"), or for people to concentrate on gaming the number rather than being more engaged ("Today's the Corporate Reporting Employee Engagement Profile (CREEP) day - I'd better walk around and smile a lot so that I get good scores!").
Far better, in my opinion, is to walk around and talk to people. Ask them how they are doing. Ask how the company can make things better for them. Listen to the answers, make a few notes for yourself, think about them, and then act.
The best places I have ever worked have been companies where the leadership took an active interest in their people. Not by sending out emails and surveys - but by talking with them, by learning their names, by acting like they care. These companies developed a culture of caring - and all levels of management participated.
Surveys are quick and cheap and easy to ignore. Spending time talking to people is more expensive. The former shows that you sort of care (at least a little), but don't want to spend money. The latter shows that you are willing to put your money and your time behind your caring. For me, that's far more valuable.
If you are in a position of top leadership at your company, ask your direct reports "Are people here engaged? Are they happy? Do they feel valued? And if so - how do you know?". Then, go out and try to confirm what you have heard by talking with a bunch of people. Finally, work on your corporate culture to make things better for everyone.