In view of the so-called 'refugee crisis' which began in late 2014, there is a growing potential demand for higher education opportunities amongst refugee communities in England and more widely in Europe. Whilst exact numbers are not certain, it is necessary to establish whether such demands can be met at all. Based on in-depth semi-structured interviews with nineteen refugees and asylum seekers residing in England, this study explores refugee background students' perceptions of the barriers to higher education and builds on previous research by including participants of varied ages, locations and study statuses -- namely, aspiring to enrol, or currently enrolled in universities. While existing previous research provided extensive accounts of barriers to access, these were presented as separate issues, where in reality, these factors rarely occur in isolation. Thus, the analytical focus in this paper concerns how these different barriers to access not only "accumulate," but also "inter-relate" and "exacerbate each other," leading to what can be described as a "super-disadvantage." This new term is proposed here as indicating the extreme degree of denial of equal access to educational opportunities experienced by those with refugee background, resulting from the added, independent effect of their migration experiences, status, and the socio-economic realities of living as a refugee. It is argued that this 'super-disadvantage' cannot be overcome without deliberate changes to outreach and support delivered by universities. These must be developed in partnerships with third sector experts and the refugee background students themselves.