I would take issue with over the 13A plug gothitjulie. It was specifically designed and rated for a 3kW load as 3 bar electric fires were commonly used at the time so assuming the plug and socket are in good condition a continuous 13A load should not be a problem.
I’d agree, but some of the ones I’ve retrieved from walls in recent years don’t appear to be upto the job, modern plastics seem to melt where the old bakelite would just shrug it off. One I used very recently I found the ends of the live & neutral pins got hot, that’s about not enough contact area so suggests the shape of the tangs inside are wrong. If you look at the online market sites it doesn’t take long to find the non-approved & fake sockets, & people have been installing them for a few years now. Check before you use them, I had an electrician friend test all the sockets in my home when I moved in & we replaced a few of them that a previous owner had installed against regulations.