Ooh - pleased the purple is something lovely, as my daughter is already very attached to it (as she is to anything purple).
A bit of stubborn googling has revealed the little white ones are allium triquetrum, otherwise known as the three cornered leek or onion weed.
This very much explains why bits of my front garden stunk of onions while we were gardening although there are a lot less as we may have ripped them out thinking they were selfseeded chives
Very excited to see what the suspected nectaroscordum does!
I may be you. Or are you me?