Bramwell was awarded the 2010 Holweck Prize of the British Institute of Physics and the Société Française de Physique (SFP) for "pioneering new concepts in the experimental and theoretical study of spin systems".  He shared the 2012 Europhysics Prize of the European Physical Society Condensed Matter Division "for the prediction and experimental observation of magnetic monopoles in spin ice".  He is a Fellow of the Institute of Physics.
In 2010 he won the Times Higher Education research project of the year for "magnetricity",  and was named by The Times on their list of the 100 top UK scientists.