The standard classification system for different types of business uses the concept of "Retail sale in non‑specialised stores with food, beverages or tobacco predominating". This makes two important distinctions: between non-specialised, and specialised shops (Sainsbury's vs the local butchers); and between shops that are mainly concerned with food (Waitrose) and shops concerned with other stuff (John Lewis). It still covers a wide range of different types of business - from a hypermarket to a cinema kiosk (including village stores, NAAFI shops, confectioner / tobacconists, and old-fashioned grocers).
In this context, OSM contributors make widespread use of "supermarket" and "convenience store" to describe non-specialised food shops. There are a few tagged "kiosk", "general store" (in various spellings), or "grocer" (in various spellings) but these only amount to about 2% of the total in this area. There is only a smattering where different shop types are combined in forms such as "convenience;alcohol".
The retail experts, IGD, reckon that there are 91,500 stores selling groceries in the UK, of which almost 8,000 are supermarkets (or variants), and more than 48,000 are convenience stores. About 6,500 of the convenience stores are on forecourts. Most of these will probably be marked in OSM as a petrol station, rather than a shop. That leaves nearly 42,000 convenience stores that we should be able to find. However, this might still be over-stating things a bit. The Association of Convenience Stores reckons that there are 33,500 convenience shops in the UK.
Across Great Britain I can find 5,849 supermarkets in the OSM database, and 6,928 convenience stores. So on face value, current coverage of supermarkets is about 73% and coverage of convenience stores is about 16-20% (depending on what baseline we use).
Normally a convenience store is quite a small store, with extended opening hours, while a supermarket is larger, and opening hours are more tightly controlled. In the UK, shops smaller than 280 square metres (about 3,000 sq. ft.) have greater flexibility on Sunday trading hours.
Where a shop is added to OSM with a building outline we can get a rough idea of the floor space, and we can use 3,000 square feet as as way of distinguishing convenience stores and supermarkets. There's no point in being rigid about this, but in general a "supermarket" with a floor space of less than 3,000 square feet is probably a convenience store, and a "convenience store" with floor space of much more than 3,000 square feet is probably a supermarket.
Where I can measure them, the average floor space (actually building footprint) of a convenience store in the OSM database is 2,000 square feet, and the average floor space of a supermarket is 43,000 sq feet. Both are well inside the right range. However, about 4% of features tagged "supermarket" could be in the wrong category, and about 20% of features tagged "convenience store" could be in the wrong category (though most of these are still quite small). Re-allocating these according to size rather than tagging would take supermarket coverage up to almost 90%, and convenience store coverage down to around 14-17%.
The bottom line is that coverage of supermarkets looks pretty thorough - the majority are in the database, they can easily be identified, and tagging is pretty consistent. Coverage of convenience stores is better than for most types of shop, but could be more thorough. Many can easily be identified in the database, but some of those might better be tagged as "supermarket".
According to the Department for Transport, most of us are within 10 minutes of our nearest food store, and within reasonable travelling distance of 3 or 4. The chances are that at least one of these is in the OSM database, and at least one is still waiting to be added. The missing ones are likely to be some friendly local convenience store - not some massive supermarket chain. Which hardly seems fair.