Is there any such career as a medical researcher?
Finding jobs in medical research that are attached to neither hospitals or universities is going to be difficult. Most career researchers will either teach (in a university) or under take professional practice (in a hospital for a medic). 

You don't say if you have a PhD or not. Generally, if you want a job in medical research outside a hospital, you will definitely need a PhD. 

There do exist independent/third sector research institutes that neither teach, nor are involved directly with patient treatment. In the US, the obvious example is the NIH facilities at Bethesda, the Sanger Institute/Crick Institute in the UK, or the Max Plank institutes in Germany. You might also find there is some medical research directly for government agencies (e.g. the civil service in the UK).

However, getting a job at one of these institutions is very difficult, as many, many people want to just do research. 

Of course, the final option for medical research outside medicine/academia is industry.