Can you wire a 240 volt oven to a 13 amp plug?

From your question, and the terminology used, you appear to be referring to the UK residential electrical system. The following answer therefore refers only to a UK installation.

Most ovens ('cookers') are designed to operate on a separate circuit with its own circuit breaker or fuse (e.g. 30 A for ovens up to 12 kW, or 45 A for ovens above 12 kW). Trying to operate such a oven from a 13-A circuit will simply cause the plug's fuse to operate, disconnecting the oven from the supply. So, while the oven will be protected, you won't be able to use it as it will keep blowing the fuse in the plug! It certainly won't melt the plug, as suggested in the original answer.

However, some small, countertop, ovens (e.g. the 'Baby Belling' brand), which are specifically designed for use in the kitchens of small flats or apartments ('bed sitters') are specifically designed to run off a 13-A plug.