This is a hard one to answer, as we don't seem to have much info on the 14th century Portuguese ships especially compared to fifteenth century ships. The same goes for Anglo-Portuguese connection where for example you can find a nice article by Wendy Childs "Anglo-Portuguese Trade in the Fifteenth Century", but nothing of such for the 14th century. I would love to someone to chime in with recent studies completely refuting my claim of lack of info, but I do not know if such exists.
The main problem with identifying the ship types is our inability to match the nomenclature (when we even have it) with some archeological remains or a contemporary depiction or even a textual description, all three of which seem to frustratingly not exits for fourteenth century Portugese ships. Even the nomenclature we do have is vague. The main word to mark ships was the "nau" which is as generic word for a ship as they come, literally meaning ship. It does seem to usually refer to the larger sail (cargo) ships, and smaller ships had often different designation. The word Nau in the fifteenth/sixteenth century was - when not used in its wider meaning - usually used to denote ships of what we today called "carrack" in English. However it would be wrong to suppose the same type of ship existed in the fourteenth century. It is more probably that the word nau then referred to a proto-carrack at best (some features existing but lacking others like multiple masts), or a cog like vessel the most likely.
Other types of Portuguese ships we know existed are barca and barinel but all works I found are frustrated by the lack of info from them. E.g. in Vasco da Gama's Voyage: Myths and Realities in Maritime History by Francisco Contente Domingues, writes the following:
We really do not know anything about the barcas and barinéis but it is an accepted fact that they used square-rigged sails because the caravel used lateen sails. And this is just about the only thing that can be said with certainty about this ship. Since the lateen caravel was said to be different from any other vessel, all that was necessary was to confirm details of earlier ships and then describe the caravel as being different from them.
To which Richard Barker in his article Shipshape for discoveries, and return adds that barinel was likely clinker built instead of carvel. This is quite likely although it must be mentioned his "evidence" is a line by Fernando Oliveira who (quote from Barker): "states that barcas were little different from the trincados of Galicia, which fairly clinches the matter." But Fernando Oliveira was writing in second half of 16th century, almost 200 years later and by his time barinel may have changed drastically.
Another ship type that appears in 14th century is caravela, albeit this denotes the small (likely coastal) fishing boat. it is universally accepted that caravel in the form of exploratory vessel appeared only by the 1430s-1440s. As such it is unlikely that caravels of 14th century looked like those, and that those would be used in English trade.
As for the trade it self, going from Childs article about the fifteenth century it seems towards the beginning of the century it was modest but rising. If we assume (and perhaps we shouldn't!) that the trend was continued from fourteenth century, it would mean even less activity then. In the first decade of fifteenth century as little as a dozen Portuguese ships yearly was the norm, and those most likely included Portuguese ships just stopping at England (Southampton) while continuing to Flanders. Childs offers more numbers of Portuguese trade in later decades and mid century, but I suspect we are now too far from 14th century to make assumptions and guesses based on those.