Acceptance of refugees and asylum seekers will be unchanged.

"How can anyone possibly know that when no-one knows what the full effects of brexit will be yet?"

Because the UK is signed up to the The Protocol Relating to the Status of Refugees.This is a key treaty in international refugee law which entered into force on 4 October 1967. 146 countries are parties to the Protocol. The earlier 1951 United Nations Convention Relating to the Status of Refugees placed both temporal and geographic restrictions on refugees. Interestingly the US is a signatory to the earlier convention, but not the later Convention.

The principle of non-refoulement, which prohibits the return of a refugee to a territory where his or her life or freedom is threatened, is considered a rule of customary international law. As such it is binding an all States, regard-less of whether they have acceded to the 1951 Convention or 1967 Protocol.

A "migrant" is anyone who seeks to move overseas. A "refugee" does so in conditions where they have been forced from their homeland. And an "asylum seeker" is someone who says he or she is a refugee, but whose claim has not yet been definitively evaluated.

Thank you Iains. And for the benefit of those who cannot understand plain English.
The above agreements were entered into before the UK became part of the EU. Us leaving the EU should have no effect upon these agreements.