Also, this will vary with subjects and funding bodies, but the bulk of PhDs will start in October or January, so if you do find a suitable short course, take those as potential finishing dates.

One last tip: communication skills sounds very much like the sort of thing offered as a transferable skills course as part of a PhD programme, so if you can't find a stand-alone course, then look at the skills programmes in your prospective Universities. Interviewers seem to like it when you show an interest in these transferrable skills programmes at interview, and they also like asking what your weakness is- so being in a position to answer that with, "I'm not very confident in my presentation skills at the moment, but I've looked at your transferable skills courses and see I would have the opportunity to improve in this area" would not put you in a bad position.

In fact, when potential supervisors wanted me to come and meet them in advance of the department's formal interviews, I explained that I was currently working so they arranged to meet me early on the morning of the interview instead. They were pretty understanding, and I felt a lot happier in my applications having spent the few months since my MSc working- not even in a relevant field, but able to talk about some "tranferrable skills" developed- than if I'd been twiddling my thumbs waiting for the PhD to start; but if you're in the lucky position of not needing to be in paid work, then you're incredibly lucky because you can do internships/volunteering and get some really relevant experience.

To be honest, so much of the PhD application process involves waiting around for supervisors etc to respond to your emails, if you treat it as a fullt-time occupation you'll go mad waiting. As long as wherever you're working is understanding enough to give you time off- and here again, voluntary work could be slightly more flexible- for actual interviews, it should be fine.

Is another course really the best thing to be doing to help you get a PhD, or would some work experience (voluntary if need be) be better?
This depends on your subject area and previous experience, but if you have a Masters then courses/qualifications is unlikely to be your main area of shortcoming as a PhD candidate.
If you really mean communication in the transferable skills sense (rather than specific skills gaps in english or IT, in which case try adult education evening classes) then most employment/volunteering can be used to work on and demonstrate this. More specific suggestions would depend on your subject.

So far I've limited myself to reading these fora but thought it was only fair to mention this...
I've spent the last 6 months doing admin temping in a mental health NHS trust- which for me was just the first thing the agency found, but might be more suitable for you- at least you'll be in contact with practicing psychologists, and surrounded by books and journals- even if you're only typing up other people's reports and minuting what other people say in meetings, if you're doing admin work anyway it could be better to be doing admin temping in a related field. I know this agency have a lot of bookings in that NHS trust but I'm not sure if I'm allowed to name them on here?
(And I came to them with very little actual admin experience, they just gave me their standard computer tests to do and realised that I had picked up those skills during my degree.)