No, @VeryGoodVeryNiceChickenNugget, they won't reverse Brexit.
There are a number of reasons for this but the main one is that rejoining the EU would require a new EU treaty which would have to be ratified by all the other member states. So any one of 27 other countries could say, "No, we don't want the UK to rejoin" and that would be it.
In at least four of those countries a referendum is needed to ratify any new EU treaty, so it wouldn't even be up to the government of those countries. For example, the Macron government or its successor could say yes to us rejoining but if voters in France profonde say, "no, fuck off", France can't ratify the treaty.
So the difficulty with rejoining is, what order would you attempt to do it in?
Would you negotiate with the EU27 and hold referendums in several other countries to decide whether the UK should be allowed to rejoin and then have a referendum in the UK to see whether British people want to? And risk that after all that, and all the countless millions of euros spent establishing whether we should be allowed to rejoin, we say, "thanks but no thanks"?
Or would you hold a referendum in the UK and take the risk that a clear majority of British voters vote to rejoin, and then the EU27 say no?
Unfortunately, whilst a vote to remain in the EU needn't have settled the matter for all eternity (in the sense that we could have voted to remain and then voted to leave ten years later), actually leaving is permanent. Once you've left, even though there is a theoretical legal path to rejoining, in practice it's impossible.
That's why Labour won't attempt to take us back into the EU, because it's not within their power.
They could negotiate a closer trading relationship with the EU and restore free movement between the UK and the EU if they were politically motivated to do so. We could probably be more like Switzerland. But that's as close as we are ever going to get to rejoining.