I have this same problem with Opera beta 42.7.2246.114996 with "desktop" user agent.
The URL that the default Google search engine generates for a search for "fun" is this, which exhibits the reported problem:
This URL exhibits the expected behavior (ability to click to different pages of search results):
My suspicion is that the URL that Opera generates doesn't properly work, causing the problem.
A (poor) solution is to add Google search to the search engines (long press on text box on www.Google.com) and then select that instead of the pre-added google search. Downside being that you can't set the default to your custom search engine, so you have to select from the search engine drop down every time.