I went last year - it was less formal than I expected but there was also a big range in formality. I wore a printed dress that just fell below the knee and then a plain blazer which was perfect for the weather.
With shoes, I'd suggest a low pair of wedges - it is a garden and the ground isn't perfectly flat, and your friend will most likely be on her feet most of the day. Something like the Jena shoes here mini wedge is ideal, I think. Obviously that particular style might be a bit tricky with tights.
Hobbs are good for dresses too - there's a few around at the moment that I think would be good, depending on length and your friend's colouring. LK Bennett too - maybe something like this? In my experience dresses that nip in and then kick out at the waist work best with blazers/jackets, but that might be more to do with my shape...
Last year Debenhams or Marks (I think it was Debenhams) had a grey skirt suit in a chiffony fabric with large cream spots - skirt, jacket and hat. I saw about five women in it, and they all looked great.
My mum swears by ghost, episode and phase eight for things like this, and often reuses them for other summer parties/weddings. The most sensible way of doing it I think is to buy a dress you can wear again and then get a nice blazer or jacket that you could wear again, but with less formal things.
And don't panic! I nearly got bullied into coerced into buying a cropped, navy blue, jacquard jacket with a single central button from Jigsaw. It made me look like a triangle, with a circle stuck on the bottom where my tummy escaped wasn't covered. The woman in the shop told me it looked nice, and I nearly fell for it. Texted my friends a photo and they set me straight! Regardless if someone tells you something is "ideal" garden party wear, if she isn't comfortable don't buy it!