I recently happened across an estimate of 1.75–2.25 million in 1086 based on the surveys of the Domesday Book, which was essentially a tax assessment made in that year. I found this citation in Pelteret's Slavery in Early Medieval England, and he was citing Salway's Roman Britain, which I have not myself checked. I suspect that these figures ultimately derive from the seminal researches of Henry Darby. Since I've been tracking down these figures for my own purposes, I'll take liberty to note that about 10% of this population was registered in the Domesday Book in a slave status, down from an estimated 30% on the date of the Norman Conquest in 1066, implying that England had some 600,000 slaves upon the arrival of William the Bastard (later: 'the Conquerer').

Regarding the estimates of Danes/Northmen, the largest indication of viking presence is a fleet of 350 ships recorded in the Anglo-Saxon Chronicle for 851. There's reason to be suspicious of these numbers—3 ships in 787, 33-35 ships in the 830s, and 350 ships in 851 make for a nice exponential curve. But if we take them to be accurate, and if we presume the average ship was about the size of the medium warship dug up at Roskilde (known to archaeologists as Skuldelev 5), then we're looking at about 30 people per ship, or up to 1500 men in the raiding party of 851.You might reasonably assume the Anglo-Saxon Chronicle had embellished the number of ships that arrived in 851, resulting in a smaller war party, or equally you could assume that the average warship was closer in size to Skuldelev 2 and carried 70, doubling the size. Either way, we're looking at roughly 1000-3000 vikings in the largest reported viking fleet. Amid an indigenous Anglo-Saxon population of roughly 2,000,000, that's a drop in the bucket (0.05-0.15%) ... but it's a drop that came with pointy things and was considered very scary, so it had a much deeper cultural impact as measured, for example, by the spread of Norse place-names across northern England.