First up is car insurance. You cannot legally drive without insurance, so you do not have the option to not buy, i.e. to decline to enter the market, which is supposedly a characteristic of free enterprise. This means that car insurance cannot be presented as a preference: a choice that demotes other potential expenditures based on the utility that accrues to the individual consumer. Given that you must enter the market under duress, the advertising and management overheads entailed in convincing you to choose insurer A over insurer B (or market comparison site A over market comparison site B) are largely waste. They do not grow the total market or persuade consumers to substitute car insurance for apples or golf clubs. They merely distribute a fixed revenue between different suppliers.
Premiums must reflect the ratio of possible claims to pool value (i.e. the sum of all premiums). The lowest ratio comes with the largest possible pool (this is simply maths), so premiums for a single national scheme would be lower, ceteris paribus, than two or more private schemes across the same population. A single national pool would have lower overheads, not just due to reduced expenditure on advertising but because of management and administrative efficiencies - i.e. scale effects. The argument that a public body would be less efficient than private provision is ideological and depends on both the theoretical incentive power of consumer market exit (which is not possible if insurance is mandatory) and the belief that supplier competition will reduce overheads, despite these ultimately reflecting pool size.
The second candidate for nationalisation is pharmaceuticals. This is not a free market today, if only because the state sets priorities for drug development through public health policy, IP licensing and the law. In a truly free market, improved strains of cocaine would be an R&D priority, simply because these would produce larger profits for pharmaceutical companies than a vaccine for the Zika virus. Having seen the poor job that incentives do in encouraging research in areas that the state prioritises (e.g. antibiotics vs chronic drugs), the state is increasingly demanding of the pharma sector (e.g. the recent UK O'Neill Commission) and may even become coercive. While the history of Big Pharma has obviously centred on large private firms, it is worth remembering that most of these have worked hand in glove with the state, both in terms of R&D (e.g. exploiting academic labs) and securing sweetheart deals for national monopolies or (in the UK) NHS supply.
The conflict between the common good and privilege is gradually leading to a distinction between "societal drugs" and "consumer drugs": vaccines for children on the one hand, expensive cancer treatments on the other. What is likely to happen is not that Pharma as a whole will be nationalised but only that part of R&D dealing with "societal drugs" - i.e. the high-cost, high-risk element that business might be happy to avoid. The manufacture of societal drugs might still be outsourced to Big Pharma, essentially through the issue of "patents" in the original sense of that word, but the falling cost of drug manufacture means that production would probably shift to developing nations, which is where we're also likely to see the manufacture of "legal highs". The boundary between licit and illicit will become ever vaguer, with Big Pharma increasingly pushing that boundary to increase profits.
The third candidate for nationalisation (and returning us to where we started) is transport. Those who demand the nationalisation of the railways are too modest in their ambitions, not least because they forget that the road network is already 99% nationalised (there are very few private toll roads). Privatised transport "services" are essentially parasitical businesses that make use of public infrastructure, from airlines that depend on a commonly-managed airspace to bus companies that gripe about road tax. While it is possible to present car-hire (whether black cabs or Uber) as a genuine market - i.e. as opposed to a de facto monopoly in which winning contracts, rather than service delivery, is the road to profit - this can only be done by ignoring the public subsidy represented by roads and traffic lights.
The argument for nationalising the railways is not that this will necessarily lead to less overcrowding, cheaper fares and better sandwiches, but that transport is a public good and should be managed to maximise public benefit. This means getting rid of first class carriages (whch increase profit per traveller at the expense of reduced traveller numbers), simplifying fares and advance booking (a major bugbear of passengers), and binning all the corporate branding, affiliate marketing and other bollocks that taints the experience of getting from one place to another. It also means rehumanising the experience of rail travel in the UK, which is less about designating "quiet carriages" or apologising for delays and more about not treating people like cattle.
Despite all the media fluff about Corbyn's supposed hypocrisy and Branson's cheek, what stood out in the video of the Labour leader sitting rather forlornly on the floor while reading a copy of Private Eye was how typical this vignette was of the routine humiliation that all passengers are faced with unless they pay a premium for a reserved seat or a first class ticket. We seem to have become inured to this over recent years, treating an uncomfortable and often unpleasant experience, for which we pay a lot of money both directly and indirectly, as if it were a form of penance or an unavoidable tax (like car insurance). Ending the humiliation is as good an argument for returning the railways to public ownership as I can think of, so perhaps the case is finally more ethical than pragmatic.