The most common problem with not being able to send email is where an email client/app (such as Windows 10 Mail) screws up the outgoing ('SMTP') server settings. However, as you're bypassing those anyway (by using PlusNet's own website) that can't be the cause of your problems here. So the fault is either with your browser or 'at their end'.
To check whether it's a browser problem, trying logging into your email using a different browser. (e.g. if you normally use Chrome, try Edge, simply because it's already on your computer). If you can then send mail normally, you'll know that the problem is with your main browser. (In which case, try clearing its cache. If you need instructions, please tell us which browser you use).
If you can't send email using a different browser, the problem is definitely 'at their end' and you'll have to wait for Plusnet to fix it. As a short-term workaround though, if you've got urgent email to deal with, you could set up a new email account with GMX
https://www.gmx.co.uk/ and configure its 'mail collector' facility to copy incoming mail from your Plusnet one to your GMX account. You could then send any replies, or other outgoing mail, from that GMX account.