New site meets lack of knowledge

I guess you'd need quite a bit for an allotment?.... Is this something I go to a garden center for?

Nope you don't need huge quantities of lime but if you buy it in 25kg bags it works out cheaper, I'd avoid garden centres most seem over priced try small hardware stores or allotment shops etc. even a local agricultural merchant may be able to supply a bag.
You should only really lime the area that your brassicas are going in, on a 3 yr rotation you'll probably cover the majority of the plot, about a handful a sq yard does me fine.