Private Blood Tests are available in Reading through Blue Horizon Medicals at the Dunedin Spire Hospital. 22 Bath road ,Reading West Berkshire . RG1 6NS. 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.