A second property is assessed as means based on the value of the property minus any outstanding mortgage, rather than the rental income.
Entitlement will depend on the scheme you're applying for, any income or other savings you may have, the assessable value of the property, plus any other rules that apply to the individual scheme.
What exactly do you mean by "Social Welfare", it covers a multitude of payments not all of which are means tested. See the Stickied Key Post. If it's Jobseekers Benefit then no your rental income doesn't come into play. I'm not sure what the implications are for other payments.