Well I managed to solve the problem or so it seems. Apparantly in my case the WordPress cURL transport method needed a ‘reset’.
Here is what worked for me:
In another thread I found a reference to the Core Control plugin which allows http debugging and tweaking. I installed it and disabled cURL.
Then everything started working again. When I later enabled cURL again it kept working.
No idea why exactly but it seems the plugin solved the problem.