It’s fairly difficult to share content between sites in a multisite network so this will buy you some efficiency by making things easier to maintain, but you will still have to find a way to share or copy content around.
To share content between sites you can look at RAMP by Crowd Favorite (getting a little long in the tooth, but we use it with some customization), or WP Site Sync (a new one but coming along rapidly), or keep an eye on VersionPress as they plan to address this need at some point. It can be done (the sharing) but it is not always simple and straightforward on a site with a lot of interdependencies between pages, so consider carefully before you commit to this approach.
Another approach would be to have one site and structure the pages so the content that is unique to a region is under a parent page for that region, which would give the appearance in the URL of a subdirectory, eg, if the URL for the UK events page should be mysite.com/uk/events/ then make the events top page a child of the uk page.
That way if you want one central blog, you can just use the posts for your mysite.com as the blog and it only has to be in one place, you don’t have to ship it around between multiple site, put it in a separate site, or cross link or redirect between the three sites to get people to the blog.
There is a great post on how to determine when to use multisite by Mika Epstein called “Don’t Use WordPress Multisite” that would be worth reading, and a little more from when Mika talked to the Director of Engineering at Wired about why they don’t use multisite.