The circuit the appliances are running on, will most likely be a 32A ring main and shouldn’t cause a problem.
Can you take a photo showing your meter cupboard or box particular showing…..
1-incoming main supply and electrcal meter?
2-the consumer unit for the EV charger?
3- The tails (thick cables) coming from the meter to you house consumer and where they split to supply the EV coinsumer uniy.
For now I suggest for safety reasons not to use the charger, as there might be a loose connection, which the emergency electrician should have checked/picked up on.