Is there a reason you don't want to take the BMAT/UKCAT? You can always take them and if you felt you did very badly, apply to another course, either in the main period or through clearing. For GEM courses Nursing degrees are not always accepted as having the necessary scientific background - usually they emphasis students having a strong laboratory science based degree (possibly specifically in biosciences) rather than a clinical course. The latter is rarer and is more commonly undertaken as a career change later in life, rather than as a plan at the outset.
I would suggest taking the tests, applying to medicine + 1 other (probably a biomedical science course being the most relevant and offering the most options - several have "transfer into medicine" schemes where pending excellent performance in first year a select few are allowed to progress to Y2 medicine. Others have guaranteed interview schemes for the offering university or a partner universities GEM course - and SGUL blends the two, giving some students on the BMS course an opportunity to pursue a more clinically oriented course and then enter into their GEM course in Y2 (which is highly unusual, and has the benefit of allowing said student to complete BSc + GEM in the same length of time as a typical MBBS). These, like GEM, are highly competitive - more so than entry into a standard MBBS (on that note it's worth noting many GEM applicants include "standard" courses in their applications, or apply to universities which consider their application for both the GEM and standard course, in order to maximize their chances of getting a spot, regardless of financial implications).