I have just started using Google Cloud Storage services. I have manage to upload a file but I can't see from the developer console how to delete it since the Delete button is not active. I am using the default bucket

What fixed it for me was going for a free trial version. I could not use any of the buttons with the default version (no billing set). As soon as I entered my credit card details the buttons came back to life.
If you decide not to do the free trial or the issue persists after signing up, you might find these commands useful:
gsutil acl ch -u "your-email":O gs://your-app-name.appspot.com
gsutil acl ch -g "google-cloud-storage-id":O gs://your-app-name.appspot.com
You can find the Google Cloud Storage ID in Developers Console -> Storage -> Cloud Storage -> Storage Settings under Project Access tab.
Consult the documentation for more info https://cloud.google.com/storage/docs/gsutil/commands/acl
gsutilto fix the permissions using a project admin's account. - tx802