I am about to start a fully funded MRes in Neuroscience and the project (focused on treatments for opioid abuse) will include a systematic review and meta-analysis of the evidence before the actual quasi-experimental part.

My institute would like to get me trained up for that and send me on a course. I initially planned to just take one at my own university, but my supervisor and most people in the institute seem to have a very strong opinion that a lot of training on systematic reviews out there is basically ****, delivered by people who think they are qualified to do it but actually aren't :D They want me to get trained to a high standard (the word 'Cochrane level' was thrown around) and my task is now to find a good course, preferably one that lasts several days, and offers decent value for the money. I have found three so far (York, London School of Hygiene & Tropical Medicine, and Nottingham), but have no idea which one is best.

So I would be grateful for any suggestions on good courses that include content on both systematic reviews and meta-analyses :)

York, LSHTM and Nottingham should all be safe bets (LSHTM is generally awesome, York is home to the Centre for Reviews and Dissemination http://www.crd.york.ac.uk/CRDWeb/). Might also be worth looking at UCL, Bristol and Sheffield. Basically anywhere that has a good epidemiology/health economics/health services research department.

If you need something more urgently, this starts next week. Johns Hopkins are highly rated for Public Health, but as with all MOOCs you'll have to see how it goes:
https://www.coursera.org/learn/systematic-review

It's also worth looking on the Cochrane sites as they may have some training resources available. Do you know what packages you'll be using to carry out the review and analysis, as this may have a bearing on what training you should look at?