Just wish to add my condolences. Tragic, but I hope time will at least partly heal what you and your family are at present going through.
As many say above, having been involved in many inquests, legal representation is a must to ensure the evidence you need to be presented is and that any contrary evidence is properly challenged as the inquest outcome will be pivotal to any subsequent claims. It does seem there is culpability on the part of the surgeon and his employers. I don't know how far along the road you are towards the inquest, but take a bit of time to select your solicitor and do a bit of research. The solicitor that represents your interests at the inquest might not be the same one that you retain to press home subsequent claims.
This may all sound a bit mercenary to you, but I doubt any monetary compensation will be adequate for the loss of your father. However, to pursue this, you will be ensuring as much as you can that what happened to your father will be properly recorded and that the likelihood of it happening to someone else is diminished, which may be some comfort.
Another reason to instruct a solicitor is that this is your father and with the best will in the world, you need the advice of someone who is not only experienced in this sort of thing, but can take a detached view.