The B.1.1.7 variant of SARS-CoV-2 first detected in the UK harbors amino-acid substitutions and deletions in the spike protein that potentially enhance host angiotensin conversion enzyme 2 (ACE2) receptor binding and viral immune evasion. Here we report cryo-EM structures of the spike protein of B.1.1.7 in the apo and ACE2-bound forms. The apo form showed one or two receptor-binding domains (RBDs) in the open conformation, without populating the fully closed state. All three RBDs were engaged in ACE2 binding. The B.1.1.7-specific A570D mutation introduces a molecular switch that could modulate the opening and closing of the RBD. The N501Y mutation introduces a π-π interaction that enhances RBD binding to ACE2 and abolishes binding of a potent neutralizing antibody (nAb). Cryo-EM also revealed how a cocktail of two nAbs simultaneously bind to all three RBDs, and demonstrated the potency of the nAb cocktail to neutralize different SARS-CoV-2 pseudovirus strains, including B.1.1.7.