This paper models the impact of the COVID-19 pandemic on graduates and non-graduates in the UK. We use a model that is designed around key features of the UK labour market: (i) graduates typically earn higher wages and enjoy greater job security than non-graduates; (ii) many graduates are employed in non-graduate roles; and (iii) most newly hired workers are recruited from other jobs rather than from unemployment. We simulate this model using an array of shocks, designed to mimic the impact of the COVID-19 pandemic. In our baseline simulation, unemployment rises to 3 million workers, of whom 2.2 million are non-graduates. Employment falls by 6.6\%, while non-graduate employment falls by 8.1\%. The real wage falls by 0.9\% while the wages of non-graduates fall by 2.0\%. We find that the temporary Job Retention Scheme (JRS) has a large impact. Without the JRS, unemployment rises to 5 million, employment falls by 20\% and real wages fall by 16\%. But we also find that the JRS has increased the loss of output due to the pandemic. We find that a ``jobs package'', designed to reduce job destruction and increase job creation can reduce the rise in unemployment from 3 million to 2.2 million and accelerate the recovery in employment. Finally, we find that a ``second wave'' of infections that leads to a reinstatement of the lockdown in 2020Q4 would deepen and prolong the loss of output and increase unemployment to 4.5 million, an unemployment rate of 13.25\%.