It depends; given how long a lot of the west held out (checking on names, it's very likely everything in Mercia west of Lichfield was still welsh even after Offa built the dyke, with some exceptions like Hwicce, and welsh was still spoken in the "english" side of the marches into the 18th century), it's obvious there wasn't much population replacement in the West Midlands, ditto for the south and northwest; most of the population replacement in the north would have been where danish strongholds were, and have come about later (I have no idea when Rheged fell but it seems to have been pretty late, and bits of it were pretty contested) while Dorset, Devon and Cornwall were conquered so late that they were more or less in Wales' position for a while, with a "native" ruled Cornwall, a still breton speaking but english integrated Devon (IIRC the charter for the diocese of Crediton gave the local name for the city as Nymed) and a thoroughly assimilated Dorset (i.e. Principalities - Marches - Hwicce).
Leaving what sources I've got, my interpretation of the data would be - depopulated east repopulated by anglosaxon immigration while surviving britons emigrate, die or rarely mingle (there's really no traces at all of breton influence in the east other than some pre-5th century inherited names and anglosaxon has too few welsh borrowings for major assimilation to make sense in the area - minor native languages in the americas left more traces on english, spanish and french than celtic languages as a whole on standard english); Lindsay, East Anglia, coastal Yorkshire, Kent, the area around Wight, Essex; limited contact zones with hostilities further inland, with pockets of resistance which both sides attest at least through legends - plantations and assimilation but also probably some destruction as a number of city ruins have been cursed by the anglosaxons and most saxon settlements in the period are upriver from the original britto-roman ones; late (7th-8th century, maybe even Somerset in the 6th century although this one is pretty much after the plague of Justinian) conquests would conform more to the idea of "germanic aristocracy with limited plantations, welsh peasantry but with limited plantations".