COVID-19 caused unprecedented social disruption the likes of which many people had not seen since the Second World War. In order to stop the spread of the virus, most nations were required to enforce strict social distancing precautions, including orders to shelter in place and national lockdowns. However, worries over whether citizens would become fatigued by precautions that constrain personal liberties made some governments hesitant to enact lockdown and social distancing measures early on in the pandemic. When people feel that their social worlds are responsive to their needs, they become more trusting and more willing to sacrifice on behalf of others. Thus, people may view COVID-19 precautions more positively and be more trusting in government responses to such an event if they are inclined to see their sociorelational world as supporting their connectedness needs. In the current study (N = 300), UK residents who were more satisfied that their close others fulfilled their connectedness needs at the start of the government-mandated lockdown, perceived COVID-19 precautions as more important and more effective than those who were relatively dissatisfied in how their connectedness needs were being met, and reported greater trust in the government’s management of the pandemic. These effects persisted in a follow-up one month later. Implications for how society and governments can benefit from the investment in social connectedness and satisfaction, and future directions are discussed.