The 'Crystalised' band were honoured to meet their Pop Idol earlier this year, and would love to contribute a track to one of her future albums.
Bass player and singer Oliver Sim told Q magazine: ''I saw her at Glastonbury [festival] and I may have shed a tear. Writing a song for her, that's the dream.
''Beyonce is very special. I think she's important. I think the super-pop thing that supposedly died with Michael Jackson is still there, with her.''
Oliver added: ''We all went for dinner. There may have been a husband of hers there. I always had a lot of things I wanted to say to her and I completely choked.''
Jamie also can't believe his band's huge success, and is ''still in disbelief'' that so many people are interested in their sound and they get to meet people like Beyonce.
He said: ''Listening to our music, I would never have thought we could do as well as we have. I'm still in disbelief.''