Yes, we have daylillies in the UK. There was a clump in my lovely Yorkshire garden (the garden was planted in the thirties by an expert horticulturalist, I was very greatful as she didn't see many of the plants come to maturity).

The ones in the photograph (thanks Bill), as described by Helen are what I know as daylilies. The others (including tiger lillies) are true lilies. I grow quite a variety, here in Scotland, they look more exotic than they are.