It will depend on your company's policy. My company has a list of doctors we can use (from GPs to specialists) and we pay a very small fee to see these. However, we can also see any doctor of our own choosing privately and then claim back approx 80% of that cost (up to a certain limit). The limits aren't particularly high but at least this provides some form of limited subsidy.
From my own experience, I've found the listed doctors are fine for simple/minor ailments (they are very much volume based and clearly just want the fee our company pays them) but for anything requiring a little more thought/attention, it's better to go "off list" and pay yourself and claim back what you can.