The Migration Observatory based in the Centre on Migration, Policy and Society (COMPAS) at the University of Oxford provides independent, evidence-based analysis of data on migrants in the UK. Their website contains a wide range of briefings, primers and reports.
The Horizon 2020 project RESPOND studies the multilevel governance of migration in 11 countries. The consortium behind this project consists of 14 partners from source, transit and destination countries, and is coordinated by Uppsala University.
The Home Office itself provides some statistics on asylum applications, resettlement and related matters, through gov.uk
This includes a wealth of historical data
The Refugee Council website offers easily accessible digests of key facts.