Unfortunately, another referendum on the EU is pointless. Even if common sense won and the Brexiteers were confounded, I very much doubt if the EU would let us re-join. Look at it from their point of view - do they really want to have the UK back, with probably a substantial minority of the country dead against the EU in all its forms? Even in the best case scenario, we'd have to wait years before being re-admitted, and we wouldn't have all the concessions we had before. Then if the Tories were to win a subsequent General Election, we might be looking at yet another referendum in the not too distant future.
You must remember that Brexit was one of the main reasons why Labour lost so many of the so called "red wall" seats. The last thing Starmer wants is to have another General Election where Brexit is a major issue.
The best course of action would be for a Labour/Lib Dem/SNP/Plaid Cymru/Green coalition to bring in PR, and gradually persuade the country to have closer links with the EU. Also, ban foreign and non-domestic ownership of newspapers and TV channels so that billionaires who don't live or pay taxes here can't peddle their anti-EU myths.