Stacey
I have to agree with Diedre.
I have an apt in La Florida and I can run lots of items on the 3.5 tariff without any trips, oven, fridge/freezer, tv, lights, kettle all at once with no issues.
Try switching things on one by one but not the oven, it may convince you that your tariff can handle what you need it to.
It sounds as though you have a fault on either the oven or your consumer unit, get an Electrician in to find the fault, upgrading your tariff would be more expensive in the longrun and the fault would still be there.