Hello Rafaela09 and Shravyo. I don`t think that any of those Universities can be recommended outright, as they are not the best, for either student satisfaction or research output. I would try and look outside London, perhaps Brunel University, which is within travelling distance from Central London. Whereas I can not speak directly for City or Goldsmiths, I can share with you my personal experience with Birkbeck, as I am a former student in the MSc Cognitive Neuroscience and Neuropsychology, at Birkbeck College. In my opinion, Birkbeck is a excessively money-driven institution, whose cunning marketing team will encourage you to signing up for what eventually turned out to be a negative experience. The course is overtly theory-based, taught by researchers with limited interest in your learning, as they were mostly concerned about a) progressing their academic career b) disseminating research for their own reputation. Even though they do advertise some PhD opportunities, these were extremely limited (and sometimes irrelevant) and felt like more like a marketing stunt than anything else.
In terms of the entry requirements, the course has actually lowered the bar for the current academic year 2020, with now accepting students with a UK 2:2. If anything, this is an example of how their selection process has become even less strict, which may be a warning sign for the quality, desirability of the course. Unfortunately, the website "admission report" does not publish the ratio of applications to offers. But, if this is anything similar to Brunel University, I would safely guess that Bikrbeck makes offer to about 90% of their applicants - this is a far cry from being a competitive course. It is a shame that most students do not understand this.
But what about the paying, enrolled students? Not many showed to care in the department. Their course tutoring was quite non-existent, with limited academic support offered to students and no encouragement to excel whatsoever. They were pretty clueless about the meaning of prime education, their duty of care towards students and due role in supporting independent learning. Unfortunately, academics were way too busy (and at times uninterested) to support you through the studies, with little opportunity for research. The College is quick at taking your money, but it offers very poor value in return. In my personal experience, the Department of Psychological Science at Birkbeck is a mediocre department, and I recommend you take your education seriously and consider better options, such York University, Cardiff, Bath, Durham, UCL, Bristol just to cite a few.
The course content itself was too broad to offer any real expertise to pursue any further post-grad study, it was mostly like an undergraduate psychology course with a biological/neurological take on psychological processes. Despite the claims in their advertising campaigns (I`d assume they spend a lot in marketing), the opportunities for research were very limited, offering very little training in any of the neuroimaging methods which underpin the teaching. The lectures were often of average/low quality - more than once taught by recent post-docs or PhD students. Interestingly, the best lectures were from guest lecturers, such as from UCL. The least useful module was the Generic Research Skills, an expensive 10-hour waste of time, focused on literature searches, phantom PhD opportunities and guidance on using the library. Despite their claims for selecting students based on merit, they will most likely accept anybody who is keen to pay the full fees. Hope this helps with your decision. Take care.