Many single ovens can plug in. Doubles generally not.
Most hobs cannot, other than a few induction types which can be set to only use a maximum of 3kW.
The description sounds like a dangerous lashup, and it's fairly likely the socket or the wiring to it has been damaged.
Why do you think there is no warranty because you didn’t install it? If it is only 6 months old it has a manufactures warranty. The Consumer Rights Act also gives you protection. Get on to the people who installed it. Howdens?
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