Internationally, Out-of-School Time (OST) provision is widely seen as providing professionally-supervised activities through which young people, living in high-poverty contexts, can improve their after-school safety, as well as academic and personal development outcomes. However, even when practical barriers to access are removed, participation is typically low, with little known from young people's perspectives about why this is. To address this, findings are reported from a qualitative study with young people (aged 11-15) living in Hollyburgh, a high-poverty neighbourhood with wide-ranging OST provision. This explored young people's endogenous views about the neighbourhood assets currently available, and those they would ideally like to have, to support their pursuit of positive educational and wider outcomes. OST provision, both currently and ideally, emerged strongly as themes, with OST providers' responses to the young people's view also being sought. In general, the young people appeared unwilling to participate in Hollyburgh's current OST provision, associating this with the supervision of those involved in anti-social behaviours and with negative perceptions of their local area more generally -- views reinforced at least partially by OST providers. It is argued that to change such perceptions, OST provision must be explicitly understood as a contextualised activity, with the potential to create spaces in which young people and professionals can co-develop more positive -- and affectively just -- discourses about young people living in high poverty areas. This presents an important challenge to the OST field's current direction of travel towards implementation science and the identification of decontextualised, replicable, "high quality" provision.