Hannah Peel recently uploaded four interesting covers to her YouTube account, including 'Blue Monday', the others being 'Tainted Love', OMD's 'Electricity' and 'Sugar Hiccup' by The Cocteau Twins. They're all absolutely charming and deserving of a few minutes of your time. Check them all out here.
I only heard Låpsley's delicate music for the first time this very morning, thanks to Drew over at Across the Kitchen Table, so can tell you virtually nothing about her, but while clicking around a few of her tunes (try this one to get the idea), I found that she too has a nice reading of 'Blue Monday' in her back pocket.