Private Blood Tests are available in Portsmouth through Blue Horizon Medicals at the Portsmouth Spire Hospital. Bartons Road Havant, Hampshire. PO9 5NP. This private and professional clinic blood test location can test patients of ages 18+ 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.