It would have been worse under Corbyn, not because we would be in an objectively worse situation but because the press would have pilloried his government for any steps they took.
Imagine a situation under a Corbyn-led government whereby, having taken steps earlier the UK not being as seriously affected by COVID as continental Europe and the US. Even if there were the same steps taken ... 80% furlough etc, and writing off of the NHS debt as Rishi did. Furlough would have probably needed to be for less time so the overall cost to the economy would be lower.
But in a country with a permanent right-wing press tinge, would Corbyn be getting lauded for having not cost as many lives as the Johnson government? No, because instead the whole "is COVID a hoax thing" would be blown up, 'well, it doesn't seem to have affected us too much, Corbyn/Labour have over-reacted and he's done what we said Labour does which is blow OUR cash again.'
And of course, subjectively it would be worse. All the stuff that was going on before AND covid too. Tories would be crowing about how they would have done better for less and because in this alternate-timeline there would be no way for us to prove otherwise.
This is the problem of the press we have and their ability to influence public opinion.