After the asylum decision
If you are granted refugee status or humanitarian protection or discretionary leave you cease to be a person subject to immigration control and you can claim all benefits subject to all other conditions. However if you are granted discretionary leave that is subject to a ‘no recourse to public funds’ condition, you will not be able to claim benefits which are public funds. You should seek immigration advice to see if this condition can be removed.
The Refugee Council, a charity that works with asylum seekers and refugees, can advise you further if your application for asylum has been rejected and you are destitute. See the information about their work with asylum seekers on the Refugee Council website.