How did Great-Britain separate from France?
"Is it possible that the oceans eroded land between them so they became separated"? Yes, sort of, but it isn't a simple story. There are several factors: (1) Rivers eroded much of the English channel, mostly during the last ice age when sea level was up to 120 metres below the present level. The Rhine actually flowed (and eroded) much further out into what is now the English channel. (2) Some have argued - though I'm not sure that I agree with them - that at least part of the English Channel was cut by glaciers. However, the main British ice sheet was further north than the channel. (3) There is sound evidence that an ice dam collapsed, resulting in a huge glacial lake outburst, which would certainly have resulted in major erosion. (4) The Alpine orogeny of late Mesozoic / early Cenozoic age, created a compressive zone across much of northern Europe, thereby flexing low-angle folding. One of the major folds was the Wealden anticline, most of which is exposed in southern England, but to a lesser extent also in northern France. Tension fractures in this anticline created an area of weakness and enhanced erosion across what is now the eastern English Channel. 

Could microplate tectonics have contributed? Good question. Certainly it is possible for the jostling of major plates to splinter off microplates, or even mesoplates - examples being the Aegean region, and the rotation of Iberia, respectively. I don't have any information on the deep geology of the Western English channel, but I suspect that tectonic thinning of the crust in that area may have contributed to subsidence and subsequent flooding.