How do I remove applications that android automatically downloads, and stop it downloading apps that I don't want automatically? I have an android phone, and every now and again, when I connect to WiFi, I notice it starts automatically downloading updates. 

However, it also seems to download/ update a number of default apps, which I never use.

I now find myself running out of space, and don't want to delete the apps I do use (banking, traveling, etc), and don't want to delete photos, videos etc, until I am able to back them up to my computer...

I have tried removing a number of these apps (Flipboard, Google Play Books,  Music, etc, Google +), but they all still seem to be there. When I uninstall them/ set back to factory, they just seem to automatically update again when I next connect to WiFi.

I don't anticipate ever having a need for these apps, so how can I permanently remove them, and remove them from the automatic updates, to free up space for messages, photos, etc?
In general, to prevent auto updates - - Disable auto updates. Google Play Store &rarr; Settings &rarr; General &rarr; Do not auto update
The apps you mentioned seem to be system apps, those that came with the device (not user installed). You can remove  those only if your device is rooted. But this is not going to help you save space as they occupy space on the /system partition, which is not available to you. 
However, you can reclaim some space by removing the updates of these apps.  Thanks to Izzy, who pointed in comments (now deleted) 



  If the apps are not to be used anyway, better approach is going to Settings › Apps and to disable them altogether – including force-stop and delete cache + data. That way: no more auto-updates for them, cleaner app-drawer, plus space saved (date + cache being removed). And don't forget that those updates indeed use up space outside /system (updates go to /data, regardless of system app or not)



If you need more space You haven't mentioned your device /Android version and whether it supports ext.SD card. If you are on Android version 6 and above you can convert your ext.SD to adoptable-storage or root your device and move apps to ext. SD. If these options are not possible, you are out of luck, barring using a cloud based service to back up