Did you purposely remove the WordPress logo on the log-in page?
There is a process in the admin dashboard to remove plugins. You should use that in the future. Usually that will avoid errors.
I’d guess, without knowing your step by step nor your building, that removing the plugin by FTP caused some tag to remain open (that breaks the WP loop) or caused a code redundancy confusing the WP php process. That error is affecting your access. The concept is similar to removing the files of an unwanted program on your PC. The files are gone but the app is not uninstalled.
I went to your site. The site seems still operative. I wish you allowed “subscribers”. I’d like to try to sign-in and see what happens.
I would try this: make a sub-domain folder, such as 2222.idesignworx.ie
Install same version WP there. Get it operative to the point you can install your basic plugins–the ones you used and like before the problem happened. No content nor design. No pages. No posts.
After completion, go to the WP folder holding the plugins folder (by cPanel) of the broken main site. I am assuming that if you design you know what and where this is. Rename that folder, such as “plugins-bad”.
Then right-click copy the newly created “plugins” folder at 2222.idesignworx.ie and paste it next to the one you just labeled “plugins-bad”. Give the hosting server a bit of time to recycle, then try logging in as you usually do. The new folder should operate as your old did. The rest of the site should remain unaffected from these steps. Hopefully this will allow you to log-in.
Do not delete the “plugin-bad” folder until you are sure the substitute folder is working properly. By undoing the steps above you can bring your original install back to the current problem state, if necessary for further trouble shooting.
The removed plugin may well have done some corruption in other places. But if you can get in, at least you can look around in the theme editor area for code breaks in the main parts.
The subdomain set-up is a good way to build and test a site. And while the horse is out of the barn, you should always be editing a child-theme version of your main theme to avoid error that leads to total loss. Some corruption does not allow recovery. How about back-up??
I hope this moves you toward a solution.