@mp10 

If the plug is not responding in any way be it simply plugging it back into the outlet then it may have died. The specs indicate the plug supporting 2.99 KW so the bulb should not be burning out the plug.

@mp10 

With a low current demand, I'm guessing it's unlikely an internal component would have burnt out and I'm guessing the smart plug must have over-current protection circuitry built-in, in the unlikely event. 

Can the smart plug be disassembled to diagnose the fault?

Is it possible to repair?

@mp10 

We don't have any information for self-repair, but our plug so comes with a manufacturer warranty.

Here is the warranty page for your region: https://www.tp-link.com/uk/support/replacement-warranty/

I believe your device should have a 2-year warranty. In that case, reach out to our support team to see what they may be able to do for you.