Is there perhaps a blockage in the u-bend? I'm certainly not an expert, but this was a problem I had. I found it very easy to unscrew the sections under the sink and clean it out.
Check that the out flow pipe is not frozen Chipchopper. Pour a kettle of hot water over it before you dismantle the U trap. It can be a messy job. Bail the sink out first with a saucepan or siphon it out if you know how. Have a bucket handy under the trap as well.
Oh, VHG... we've all done that a few times. Lying under a sink and reaching up to empty the trap into it. Plumbing makes fools of us all.........
Chippers, with the trap removed, poke down the outlet pipe with a length of fencing wire, or a straightened out coat hanger. The bung-up won't be far away.
First though, if the outlet goes to an external gully, check it's not frozen solid or obstructed in some way.
I went through all the remedies above and below the sink, only to find that a short length of plastic pipe had frozen solid on the outside wall. I sorted that with some hot water from the kettle.
Oh' well, the U bend did need cleaning though! ;-/