At 2050W the current should be well within the capacity of a 13A plug (about 8.5 amps). As Dave said though, many of the cheap plugs get worringly warm on even a moderate load.
You might not notice it on, say, an electric kettle because it's only runing a few minutes at a time. But that dryer is running continuously for an hour or more. I would echo the comment about making sure that heavy/long-term loads such as this are wired through good quality connectors (MK is an excellent choice) rather than no-name bargain basement types.
And most definitely do not run the dryer and washer simultaneously on that extension!
