The origins of NAMS dates back to the 1994 season, when the innaugural competition was won by the University of Birmingham Medical School RFC. Since then, the competition has grown and remained an integral part of the calendar for many Medical Schools throughout England and Wales, with fixtures against other Medical Schools being the highlights of their calendars. Since then, the competition has been dominated by Cardiff Medicals RFC, who have won the competition more than any other side by quite some margin, with Southampton University Hospitals RFC winning twice in a row in the 2011/12 and 2012/13 seasons. The 2014/15 season saw Sheffield Medicals RFC win the competition for the first time, and in doing so became the first time outside of the South-West and Midlands Divisions to win the competition. 

Traditionally, the teams were split geographically into 4 divisions; the South-East, South-West, Midlands and Northern Divisions. Originally the sides would play each other twice, with the top two sides from each division progressing through to the Cup Knockout competition, and the remaining two sides progressing through to the plate competition. However, in recent years, due to the decline in numbers of some Medical Schools sides, and some Medical School sides beginning to compete in local Men's league, it was decided that each side would only play each other once (with the addition of the Bonus Points rule introduced). At the same time, the South-East division collapsed due to the London Medical Schools external commitments. 

However, with the re-introduction of GKT in the 2014/15 season and the introduction of the Medical Schools Rugby League being introduced alongside the NAMS Competition, there are signals that the standard and depth of Medical Schools Rugby is stronger than ever. 

Cup Winners; 

1993/94; University of Birmingham Medics RFC

1994/95; Cardiff Medicals RFC

1995/96; Cardiff Medicals RFC

1996/97; Cardiff Medicals RFC

1997/98; University of Birmingham Medics RFC

1998/99; Cardiff Medicals RFC

1999/2000; Cardiff Medicals RFC

2000/01; Cardiff Medicals RFC

2001/02; Cardiff Medicals RFC

2002/03; Cardiff Medicals RFC

2003/04; Cardiff Medicals RFC

2004/05; Cardiff Medicals RFC

2005/06; Cardiff Medicals RFC

2006/07; Cardiff Medicals RFC

2007/08; Cardiff Medicals RFC

2008/09; Cardiff Medicals RFC

2009/10; Cardiff Medicals RFC

2010/11; Cardiff Medicals RFC

2011/12; Southampton University Hospitals RFC

2012/13; Southampton University Hospitals RFC

2013/14; Sheffield Medics RFC

2014/15; Manchester Medics RFC

2015/16; Southampton University Hospitals RFC

2016/17; Cardiff Medicals RFC

2017/18; Cardiff Medicals RFC

2018/19; Manchester Medics RFC

Plate Winners; 

2012/13; Bristol University Hospitals RFC

2013/14; Peninsula and Exeter Medics RFC

2014/15; Nottingham Medics RFC

2015/16; Liverpool Medics RFC

2016/17; Brighton and Sussex Medics RFC

2017/18; Bristol University Hospitals RFC

2018/19; Liverpool Medics RFC