UK & European electricity was harmonised in 2003. In the UK electricity should be supplied @230V - 6% +10% and @ 50Hz +/-1%, and at up to 132kV +/- 6%, and over 132kV +/- 10% (Electricity Safety, Quality and Continuity Regulations 2002).
This means the domestic voltage is allowed to vary between 206.2V - 253V quite legally.
At the lower voltage, 3500W will slightly exceed 16A. At 230V the current will be just over 15A, so the plug is already close to its working limit (I'm assuming 15A was the design spec).
A large proportion of imported plugs and leads are only just up to UK/EC standards, and another proportion are not.
I worked for a company from a country I won't mention who wanted to know how to get the CE mark on their products. I told them how to submit for tests, get the results verified and submit the paperwork and wait for approval. Their response was to ask why they couldn't self certify (ie say the product matched regulations) and put the logo on the products.
Its important to note that bumps, bangs, drops and general (mis) use can, overtime, loosen contacts and increase resistance. Continued running at high loads can lead to gradual breakdown of the plastic body which will allow movement in the connector and cause high resistance. The localised high resistance causes high temperatures.
From a quick look at the pictures, I would say that the plug has just decayed over time exacerbated by slight overloading due to supply fluctuations. If the lead is OK, and the internal connectors/circuit are OK, I expect replacing the plug will suffice, especially if you've used it OK for some time. It's important you verify that the circuit is OK and not showing any signs of burning.
Unfortunately as someone alluded to earlier, the regulations can be interpreted in different ways, and if you ask an electrician about your setup you may well get a long debate about his interpretations and warnings of various disaster scenarios that will make you want to disconnect all electrical items and wear tinfoil on your head.
However, the people here
Electrics UK
Are quite friendly and you'll get mostly good advice with only the occasional disaster scenario devil's advocate post.
If it were me, as it's already on a dedicated circuit (with appropriate protection I assume) and assuming it's performed satisfactory many times, and there's no sign of over heating in the boiler internals, I'd replace the damaged socket and plug with a good quality ones of the same type and monitor for overheating.
If you're OK to replace the boiler socket yourself, you can get a lead with commando plug to C19 plug like this (just one example)
16 Amp Commando To IEC C19 Extension | DCDI
Note though, that this kind of setup is working close to its limit, so periodic inspection is important.
Long term, I'd consider wiring the boiler direct with suitable rated flex and isolator and leaving out the plugs /sockets. Or, at least, wiring the boiler to a commando plug and leaving out the C19 plug. As per Tim's pictures.
