Hi there!
We have the exact same cables and plugs here in the UK..... (shared history!)
To try for you, I've connected a same type of lead you have shown in the picture to my MacBook Pro's charger block and then connected to the MacBook, seems to work fine, charges OK. My laptop uses the Magsafe connector and when the cable was connected, the led went green and then turned orange, just as it normally does.
Looking at the two hole connector on the UK / Singapore cable, it appears to be the same as Apple's two prone connection on the charging block.
Hope this helps