It's also confusing when platforms aren't numbered in order. Oxford has p1 by the main entrance (town side), p2 opposite p1 and p3, the north bay, to the town side of p1...
Sounds reasonable if it is the case that the third platform was added at a later time once the first two were in use. The potential confusion would have to be weighed up against the upheaval of other options such as renumbering platforms which are already in use and causing confusion to existing regular users, or having a ridiculous "Platform 0" which carries the implication it's not a platform in use for passenger trains.
I've noticed that, in the Strathclyde area, the platform heading towards Glasgow Central / Queen Street is always Platform 1, and the other is Platform 2.
Things get a bit hazy between Glasgow and Edinburgh, where Platform 1 becomes the platform going towards Edinburgh.
Is there some sort of national convention that says the up platform is always platform 1?
The convention would be that platform 1 is normally that where the main entrance is located.
The convention which decides which side gets the main entrance would generally be to do with the local transport patterns as understood when the line was built -obviously you would build your ticket office, main waiting areas etc on the side where people wait to catch their train in the morning rather than where they arrive in the evening and leave the station without hanging around. If the major city where everyone goes is actually in the Down direction as arbitrarily and irrelevantly defined with respect to London (i.e. any station between Berwick-Edinburgh or between Carstairs-Glasgow) then you're best served by calling the Down line as platform 1 - because in practice it is actually the Up line for the main service.
Many UK areas had Up/Down defined in the opposite direction at some point in the past, before their integration into a nationally regulated network had the local Up/Down abandoned for the London-centric convention.
This could yet happen again if Scotland secedes from the UK, their new railway authority might define anywhere from one to three conventions (three = Up towards Glasgow, Up towards Edinburgh, and something else for routes linking the two) which would all have UK-Scotland trains starting as Down trains and becoming Up trains at the international border.
Larger countries (apart from maybe France) have this easier because the absence of a single dominant city with terminus stations like London means there is no single national convention for Up/Down to make things awkward in the other cities. National rail in Australia, for example, is the result of links being built to bridge the gaps between four systems centred on the state capital cities of Adelaide, Brisbane, Melbourne, Sydney and Perth. A single Up/Down would be impossible to do without many conflicts, so interstate trains are talked about as East-West (Perth/Darwin-Adelaide, Perth-Sydney, Adelaide-Sydney, and Adelaide-Melbourne) or North/South (Melbourne-Sydney-Brisbane) with Up/Down only being used when referring to particular lines in those suburban areas where that is the convention.
I'm not sure what the conventions are in the other state capital cities are though - Adelaide is the only one of the four where the central station is a terminal rather than a through station.