MOOC's for failed modules in PhD applicaiton I'm applying for PhD's (from the UK) with a low 2:2 BSc and a Distinction MSc, and performed very poorly in a few certain modules of my undergrad degree (including failing two 3rd year modules) which pulled my grade down. In my MSc research project and the MSc modules most relevant to my PhD field of study, however, I obtained high firsts (80%+).

I'm taking online courses on the failed undergrad topics on edx and coursera to strengthen my previous weak points and fill the gaps in my knowledge. Is it worth highlighting this in my application, and if so, is it worth paying for the verified certificates? I'm aware of the general opinion that mentioning MOOC's in a SOP isn't detrimental but does little to strengthen an application - in my case, would it at all counteract the bad module marks?
By and large, in the UK, MOOCs completion does not help your chances of admission; they are almost entirely ignored during the admission process. The only things that are considered are your results in your accredited degree programs. Paying for a certificate will not validate your MOOC participation in any way that Universities recognise; you should only pay for a certificate if you want a certificate for yourself, they do nothing else (take it from me, I lead a MOOC). 

The good news is that an excellent MSc result can do a lot to make up for a poor Undergraduate result. How you did as a postgrad is much more indicative of the kind of PhD student you would be than your undergraduate record. Consider writing a cover letter that takes your record head on, explains how you've matured as a researcher since then, that you are ready for real research, and your MSc is proof.