The Conservatives, with the help of their Australian advisor Issac Levido, believe campaigns do make a difference. They're taking inspiration from Scott Morrison's unexpected victory in the 2019 Australian general election; Levido masterminded that campaign too.
Here is what the opinion polls said in the lead up to the 2019 Australian general election:
Like the Tories, the governing Australian Liberal party had ousted their leader, sitting Prime Minister Malcolm Turnbull, and replaced him with Morrison. Like in the UK, Australians expressed disapproval of the chaos in government.
Morrison campaigned on the economy, the opposition Labour party campaigned on climate change. Again a similar parallel to the UK.
What makes things tougher for the Tories is the disastrous Liz Truss interlude, which dented the Tory reputation for economic competance.
Sunak has retrieved the economic situation to the point where the British economy is performing better than that of France and Germany. But voters don't want to be told they're doing better than the Europeans, they want to feel the affuence in their pockets. That won't happen till both inflation and taxes come down.