Macbook: No internet access wit Safari, app store etc but works with firefox, dropbox etc?

I've been having issues with the internet on my macbook pro. It is connected to the wifi which has never given me any trouble before. The internet connection works, i can receive emails, use dropbox and access the internet through firefox. Most Apple related software however can't access it. I use safari and when it stopped working had to use firefox because for some reason it works when safari doesn't. Also, I can't access the app store or perform software updates. Whenever I try to download - or even scan - for software updates I get an error message saying there is no internet connection and when I check it, it works without fault!

I keep thinking the issue might be resolved by updating all my software but I can't do that if I can't find the updates or access the app store. I'm at a loss, has anybody had any similar issues or any ideas what the problem might be and how to solve it?