That would depend on when the change happened in time.
Had 'another party' taken over at the last election there would have been minimal time. The one thing you can be sure of would be that Brexit would have been postponed until another referendum could be run.
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Take it back further to when Mrs Dopey May lost her majority. Had that election gone to 'another party' then they would have started investing in the NHS...
Absolute speculation, neither of those things are certainties at all and especially in the case of another referendum; you can't just keep re-doing referendums every time you don't like the outcome, this is why they are not legally binding and have been the tool of fascists and demagogues.
The Labour party manifesto when May got her election included improvements to the NHS. Labour has always put more money into healthcare, Tories have always tried to cut it to give their rich backers tax cuts.
When Blair got into office the national debt was about £500 billion. At the start of the financial crisis, triggered by US banks and investments, it was still about the same £500 billion. During the banking crisis UK borrowing doubled, meaning when Labour left office the country owed just over 1 trillion, but the economy was on the way up again. Had the Tories just continued Brown's plan GDP growth would have overtaken borrowing. Germany and France did go for growth, meaning they paid back the debt. UK went austerity, GDP growth stalled meaning that the £1 trillion debt is now over £2 trillion. That is not speculation that is economic fact.
As for the referendum. The UK courts agreed that it was fraudulent and undemocratic. The only reason that the courts didn't render it null and void was because the government was not bound by the result so could do whatever it liked, providing there was a vote for it in parliament. Luckily for those who really wanted to leave the Tories were against staying and so was Labour leader Jeremy Corbyn. The referendum was worthless, used as an excuse. Day before the result, a deal would be easy and better than remaining inside. The day after they changed that to leave with no deal.
Then I'm not saying we should have had referendums until we got one I liked the result of, that is irrelevant. The important bit would have been the government pushing the issue back as far as needed and ignoring it until the covid issue was over. That would have enabled them to spend far more time dealing with the crisis that couldn't be delayed.
Even if Jeremy Corbyn had won he still wanted us to leave the EU and he would have done his best to achieve that.