Private Blood Tests are available in Southampton through Blue Horizon Medicals at the Southampton Spire Hospital. Chalybeate Close, Southampton. SO16 6UY. This private and professional clinic blood test location can test patients of ages 5+ and does have freezing facilities, meaning more profiles are available than standard postal profiles. As phlebotomy is included and the entire process is managed by professionals, this is a VIP blood test, not a DIY blood test.