A pretty low one. There were still speakers of the Cornish language, we don't have any data as to exactly how many speakers spoke this but there were a little over 5400 households in Cornwall based on the doomsday book. Some of these might be Anglo-Saxon migrants who didn't speak it and there was some Corish speakers in the west of modern Devon on the other hand so this cannot be used as anything more than a ball park estimate to judge such things. But if we take an estimate of perhaps 25,000-35000 as a very approximate estimate for the population of Cornish speakers So as a very rough napkin estimate maybe 1% of the population of England spoke Cornish.

The other Celtic language spoken in modern England would be Cumbric. Now this language was still going strong further north in the Kingdom of Strathclyde mostly in the south of modern Scotland, that had been incorperated into the expanding Kingdom of Scotland at earlier in the century although it seems likely that it still retained a significant number of Britonnic speakers in 1066. In England itself though while there were likely still a handful of tucked away pockets of Cumbric speakers when the Normans were arriving they were by now a minority even within the traditional regions of the north west of England where the Old North held out longest as independent kingdoms and maintained a distinct population. Some local pockets likely existed in fringe areas by this point where Brittonic speakers were still common but while we can guess their population was not large compared to the total population of England we just don't have enough information to make a good estimate of how many exactly.

Then on the subject of cultural exchange across the Anglo Welsh boarder it has been observed that typically speaking during this period arguably there was more human exchange in cultural exchange in that if someone moved from a Welsh Kingdom into England, particularly in order to marry into a Saxon family, they would be more likely to take up English as their primary language and teach it to their children at least in the long term. As a result we can guess the population of Welsh speakers in England wasn't very high.

In all its hard to make an accurate estimate. Probably above about 1% but well bellow 5% is about as accurate as i think you're likely to get.