There are 4 general faults with electric kettles
Standard plug-in kettles
Heating element may just "die", or sometimes go intermittent.
If it does go intermittent, the signs may seem strange. The kettle will start, get halfway to boiling, stop, and then start again. People often think this is a switch fault.
Elements are normally easily replaced and tend to cost around £8-10.
Switch units may stop switching off, or the kettle may not switch on at all.
Most kettles of this style have one switch (either at the top or bottom), but some have a switch at the top, and a cut-out type switch at the bottom. Both can be replaced.
Water gauges can be troublesome. They tend to leak. The cause is rarely the seal on the gauge, but the gauge itself, which often crazes around the point nearest the source of heat. These can be fairly easily replaced.
The flex can sometimes break up internally. This is a straightforward matter of replacement.
Similar problems to above, but with added complication of connectors.
One on the underside of the kettle, and one in the base stand unit. Careless use may sometimes allow water to get into these contacts. The fuse may then blow, or the operation of the kettle becomes intermittent. Both of these items can normally be replaced.
For further help with repairs, try www.howtomendit.com