In terms of Covid 19 testing, irregular migrants are regarded as a 'hard to reach' group, along with the homeless, sex workers, former criminals*, non-English-speaking monolingual groups, etc. They do not willingly come forward to be registered or tested; many work in the black economy so cannot afford not to work. Added to the probably adverse living conditions they experience, levels of infection are likely to be very high.
* the rumour is that Covid 19 PCR testing is collecting DNA samples, hence the low public uptake in Liverpool during the mass testing in Liverpool in November.