For the last 6 months, I volunteered in Athens at Refugee Legal Support. It was overwhelmingly clear that there are systemic deficiencies in the Greek Asylum Service and no proper welfare provisions to safely accommodate and support people who arrive to Greece in search of sanctuary. Despite EU initiatives which attempt to patch the wounds, it is common that people struggle to register their asylum claims and asylum seekers generally do not have safe accommodation or adequate support.
There have been improvements in Greece since the landmark case of MSS v Belgium and Greece in 2011, and in 2016 the European Commission declared that returns under Dublin should resume. However, it is clear on the ground that human rights violations are still the norm and returns to Greece - both of asylum seekers and recognised refugees - should cease. Given that the Home Office are attempting to return recognised refugees to Greece, RLS have created a pack to assist lawyers in such cases, including materials and precedents which should assist. The pack can be obtained by emailing firstname.lastname@example.org.
I wrote this article for Freemovement, which gives more context regarding the current conditions in Greece and argues that all returns are unlawful: https://www.freemovement.org.uk/returns-to-greece/