The UK government has made tremendous progress in controlling neonatal mortality, however more needs to be done to end all avoidable deaths by the end of 2030. Application of time series forecasting techniques will highlight likely future trends of neonatal mortality to inform public health decisions and resource allocation to neonatal healthcare interventions. This study uses annual time series data on neonatal mortality rate (NMR) for the United Kingdom from 1960 to 2019 to predict future trends of NMR over the period 2020 to 2030. Unit root tests have shown that the series under consideration is an I (1) variable. The optimal model based on AIC is the ARIMA (3,1,2) model. The ARIMA model predictions indicate that neonatal mortality will remain under control throughout the out of sample period. Therefore, we encourage the UK government to address existing socio-economic inequalities amongst other measures in order to keep neonatal and infant deaths under control.