There is quite a variety in these baskets and over time they have been given various pattern names that don't always have much logic to them. The name "May Basket" has been used both specifically (to refer to one or other of the baskets) as well as generally (to refer to all of them). Other names include Duchesse, Fleur de Lys, Maple Leaf and Diamond Point. To add a further touch of confusion, various makers have been assigned to them over time too, including Northwood, Brockwitz and Davidson.
The only one of these baskets that has an easy name which won't get mixed up is the George VI one.
http://www.geocities.com/carni_glass_uk_2000/GeorgeVI.htmlAs to maker, well neither Northwood, nor Brockwitz nor Davidson. In my opinion, almost certainly an English maker, could be Sowerby, but equally could be another UK maker. No absolute proof yet.
With regard to the spurious Brockwitz attribution (in at least one book) you can see what Brockwitz actually did do here.
http://www.geocities.com/carni_glass_uk_2000/Baskets.htmlAnd finally (I did go on, didn't I

it seems fine to me to call your basket a "May Basket". You could also call it either Duchesse, Diamond Point or Fleur de Lys if you want
