Sole Tenancy Advice

Advice please: My partner is a full-time worker and earning enough to support the family. We are currently in a situation where we live with parents and have been saving for a house but our savings do not cover enough for a deposit (although it should). Our family have sold there house and we have been asked to find somewhere to live…so this is urgent and we are panicking and scared. DOES open Rent support Sole Tenancies? I do work but not enough to afford rent asking prices and look after our 3yr old child so it would be soley in my partners name?