There don't seem to be any recent figures available online. Even the BMA website, which has loads of stuff on Covid-19, doesn't offer any figures:
https://www.bma.org.uk/advice-and-support/covid-19
However it's worth remembering that the death rate from Covid-19 among hospital staff is only HALF of that of the general population, meaning that hospitals are among the SAFEST places to be working at the moment. (It's taxi drivers, bus drivers and supermarket staff who're far more at risk of dying than the general public are).