If you are working for 30 hrs pw or more, then you are considered to be in full time employment and not entitled to Supplementary Welfare Allowance (including Rent Supplement) regardless of income.
However, if you are on your local authority's RAS waiting list (not the general housing waiting list), you may have an entitlement to Rent Supplement even if working full time. This is the only exception.
You should contact your local authority, and make sure you're on a housing list.
You may be entitled to FIS (family income supplement) when the baby is born.