The websites of organizations involved in advocacy, debate and law reform will give a wide range of information and a sense of the flavour of current debates and policy issues. It is good to keep up to date with one or two of them on a regular basis.
Here are some options:
JCWI is 'an independent national voluntary organisation, campaigning for justice and combating racism in immigration and asylum law and policy': www.jcwi.org.uk.
Migrant Rights Network works for ‘a rights-based approach to migration, with migrants as full partners in developing the policies and procedures which affect life in the UK’. www.migrantsrights.org.uk/
The Refugee Council is a large refugee agency in the UK, providing policy work and advice to refugees and asylum seekers and organisations working in that field. www.refugeecouncil.org.uk/
Refugee Action is a national charity working on access to legal advice, destitution, and refugee rights. See https://www.refugee-action.org.uk/
All of these organizations give updates on some legal issues and information on campaigns relating to law and policy.
Websites of national and international policy bodies will also be useful for getting acquainted with the wider policy field. This is only a selection:
The Migration Observatory gives general information, research papers and statistics: http://www.migrationobservatory.ox.ac.uk/
The work and reports of the Global Commission on International Migration can be seen at https://www.iom.int/global-commission-international-migration.
The International Organisation on Migration is an intergovernmental body committed to the principle that humane and orderly migration benefits society: www.iom.int.
The Institute of Public Policy Research often produces interesting material related to immigration: http://www.ippr.org/.
The Independent Chief Inspector of Borders and Immigration publishes reports of his inspections on his website. They are available on https://www.gov.uk/government/organisations/independent-chief-inspector-of-borders-and-immigration
The Minority Rights Group www.minorityrights.org/ is an international human rights organisation working to secure rights for ethnic, religious and linguistic minorities and indigenous people around the world.
You can still read Security in a Global Hub at http://www.statewatch.org/news/2007/nov/uk-border-review-report.pdf.