These things are often difficult to determine, either because sources don't match up, there is only one source, or because the number may have been approximated by the author. Take the Battle of Brunanburh, for example. The best account we have of it is in The Anglo-Saxon Chronicle as a poem (there are other sources, but no more reliable than the ASC). The record keepers were less concerned about troop sizes and movement, and more concerned with how the battle was perceived by their audience.

We can look at administrative records, too, in order to see how much money was spent on soldiers' salaries, but they are often given in bulk numbers with partial namelists attached (e.g. William received £20 plus a horse, and his men £300 plus 300 pounds of fish), so it's hard to determine how many people were in the force.

Similarly, baptismal records are sometimes available for towns that can provide a rough estimate of a given locations population over a certain period of time (though much less so pre-1066), and thus an even rougher estimate of the number of 'militarily-eligible' men that might be around in the area.

Here's an example of how troop numbers are estimated in the Byzantine Empire during the same time period. And here's one on Danish military organization. Many scholars argue that claimed troop numbers were exaggerated.

There's no good data on army sizes in England before the Burghal Hideage (and even that's not very clear), but there are textual accounts of how big armies might be. The normal examples given are Ine's definition of an army being larger than 35 men, and Cyneheard's almost successful takeover of Wessex from Cynewulf with only 84 men, but neither of these are helpful (the former isn't descriptive, the latter was an ambush not a battle). The Great Heathen Army (which I thought Vikings showed to be fairly larger than a couple of hundred but YMMV) probably was several thousands (some suggest 5000 plus camp followers). The textual accounts of hundreds of Viking ships might be helpful if anyone could decide how many could fit in one (estimates range from ~24 - 60) and assuming they're not inflated for effect. Alfred probably had between 1800 and 2700 men in his standing army based on the numbers in the Burghal Hideage (which suggested you would need 27,000 to man all the walls of the burhs). So textually, you could have several thousands in an army and that wouldn't be too impossible, but small numbers of people are described as having a large effect (in continental sources), so 200 men in the right place at the right time could be devastating. Anything over this is problematic (at least in England), mostly because of logistics. An army of 5000 men needs an absolutely massive supply line and you can only scavenge so much off the local population - the Heathen Army attacks in 894 onwards show this.