We have no comprehensive picture yet of what has happened to immigration since the ‘lockdown’ began on 23 March.
However, the following Home Office link shows that visa applications and grants, extensions of leave and asylum applications and grants all dropped very sharply during April, both due to travel restrictions around the world and staffing / interviewing issues here in the UK as a result of Covid. Refugee resettlement stopped entirely. https://www.gov.uk/government/statistics/announcements/statistics-relating-to-covid-19-and-the-immigration-system-may-2020
More up to date figures released by the Home Office at the end of last month (covering the year to June 2020) show that there were 2.1 million visas granted in the year ending June 2020, a 29% decrease compared with the previous year.
The latest comprehensive immigration statistics that we have are for the year to March 2020 (see Office for National Statistics release and our migration statistics page). We will hopefully receive more comprehensive immigration figures for the year to June 2020 in November.
However, one aspect of (albeit illegal) immigration that has increased since March is unauthorised Channel crossings from France and Belgium. We saw six times the number arriving via this route during this Summer as we saw last Summer (see our Channel Tracker).