It's a chemical fractionation process [1] on thousands of litres of blood plasma, and that's how it is still done today for those products which aren't produced by recombinant DNA. But these days there are repeated health screens and viral testing on both the donors and batches, as well as solvent-treating/ultra-filtering the products.
Maybe it is possible to process in smaller batches, but I suspect that is down the the facility producing it, and the issue was the that UK weren't able to increase their in-house production at the time.
Of course more - smaller - batches would have been more costly.