Labour's Baroness Gould of Potternewton focused on HIV-Aids diagnosis, before crossbencher Baroness Masham of Ilton highlighted "hard-to-reach" sufferers of tuberculosis.
Among those who have also objected to the plans are Friends of the Earth, Campaign to Protect Rural England, Ramblers Association, Nun Monkton and Masham parish councils and North Yorkshire Waste Action group.
Peers voted by 234 votes to 198 - majority 36 - to reject an amendment proposed by crossbench peer Baroness Masham to place a duty on the health secretary to ensure openness and transparency with patients when things go wrong.