How do I remove the 'My Orders' block that comes up on the right of the product page prompting you to order a product again?
Can I remove this via the admin at all, without going into the code?
Looking at your other posts, it appears you're using the Porto theme? Magento doesn't add those box by default.
I've had a look in the Porto settings documentation - it looks comprehensive, but there doesn't seem to be a setting to disable this functionality. As per @iWeb GazJoy's post previously - if you can identify the block you can comment it out of the XML - but you may need to contact the Porto guys directly to get that support,
Providing the porto theme does not redeclare the block under a different name you can remove it in xml like so;
Unfortunately there is not a global way in the admin area to do this so you will have to edit your local layout xml file to do it.