“Cherry picking on stilts said one critic of Labour’s idea for the UK negotiating stance. They want “full access to” EU markets maintaining the “benefits of the single market and customs union” . The UK should also be able to “negotiate agreement of new trade deals in our national interest”, and should not be a “passive recipient of rules decided elsewhere by others”. There’s a good series of contradictions for you in a few sentences.
You cannot be in a customs union with a Customs Union and negotiate your own free trade deals on the side. You have to impose their common external tariff on everyone else. Nor is it at all likely that you can stay in a customs union with the rest of the EU without having to accept their rules.
It is unlikely the EU would offer us membership of a customs union without requiring that we accept their rules, and without demanding payments and continued freedom of movement. In other words a customs union would look much like membership of the EU without a seat at the table to be outvoted in person.
Meanwhile it is Groundhog time again in the Commons on this issue. We have twice had important debates and votes on whether the UK should stay in the customs union or not. (Amendments to the Queens Speech and to the EU Withdrawal Bill) Twice the Commons has decisively rejected this idea. Now some MPs want to do it again as a amendment to the Trade Bill. I do not see the point of doing it all again, and would expect the government to win another vote on this, even if this time Labour is on a whip to support the customs union instead of whipping to abstain.