Can I use an extension lead with my plug-in kiln?

No - whilst the extension lead may well be rated at 13 amps it is not designed to deliver the maximum current at the full supply voltage because of the thickness of the cable. This voltage drop will result in the cable becoming overheated, and a potential fire risk, and the kiln failing to achieve the desired firing temperature. All kilns, irrespective of size, require the supply current to be at the stipulated level as on the data plate, and for this to be at the full specified voltage, so power supply installations need to take into account the potential voltage drop and be ‘uprated’ to compensate.