Emergency
You can smell burning coming from a plug socket: a sign of potential electrical fire.
Your consumer unit or fuse box smells of burning plastic or hot electrics. Treat it as an electrical fire risk: turn off the main switch if safe, evacuate if there is smoke, and call an emergency electrician.
A chemical, acrid, burning plastic smell is coming from your electrics.
High risk
A plug socket in your home feels hot when you touch it, even when nothing is plugged in.
The plug on an appliance gets hot or very warm when it is in use.
A light switch in your home feels hot or very warm to the touch.
Your plug or socket has brown or black scorch marks, discolouration, or signs of charring.
A melted plug means the plug or socket overheated at a poor connection. Switch that circuit off at the consumer unit, do not pull out a hot plug, and have an electrician check the socket before anyone uses it again. If there is smoke or flame, get out and call 999.
You can see smoke coming from a plug socket: this is a fire emergency.
Your extension lead cable, plug, or sockets are getting hot during use.
Describe the job and get a fixed price from a local electrician.