Be aware that not having a third maths/science subject (Cambridge doesn't tend to count psychology as a science) could limit your opportunity to be 'pooled' at Cambridge. To the extent of my knowledge (and I'm not an expert here, so please correct me if I'm wrong), this is what happens if the college you apply to is oversubscribed/cannot accommodate you, but still thinks you would be an asset to the University and so puts your application forwards to be considered by other colleges. If your A-Levels don't satisfy the requirements of all colleges, some may not be able to consider your application from the 'pool', so you could be restricting your overall chance to get into the University.
Also, I would assume that quite a few Cambridge Medicine applicants would have, at minimum, A-Levels in biology, chemistry and maths; many will be studying four A-Levels. Maths is generally considered to be a harder subject than psychology and so some Cambridge Colleges will prefer maths, given how competitive Medicine is.