Apart from ploughteams, livestock were only recorded for eight counties (or parts of them), and then only the animals owned by the lord. Historians have struggled to extrapolate the partial returns to national totals, but the results aren't very conclusive. For what it's worth (which isn't much), the numbers might suggest something like a quarter of a million cattle (excluding ploughbeasts), a similar number of goats, three million sheep and half a million pigs, but I'd take all that with a very large dose of salt indeed: sheep numbers in particular are widely thought to have been a good deal higher, and the same may well go for cattle.
We can be on surer ground in saying that numbers rose appreciably over the next two centuries or so, though how much and to what level is again open to debate (peak 14th-century wool exports suggest perhaps 10-15 million sheep; some authors suggest more though I incline to the lower end of the range). No national livestock count was undertaken until the start of annual agricultural returns in 1866, and even then the first few years' numbers may have been deficient.