Private Blood Tests are available in Southend on Sea through Blue Horizon Medicals at the Wellesley Spire Hospital. Eastern Avenue, Southend-on-Sea, Essex. SS2 4XH. This private and professional clinic blood test location can test patients of ages 5+ but does not have freezing facilities. As phlebotomy is included and the entire process is managed by professionals, this is a VIP blood test, not a DIY blood test.