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The Tory MEPs after the 2015 GE withdrew from the Centre Right coallition within the European Parliament and joined a grouping which includes the German AfD MEPs. Merkel will never grant any concessions to May, or anyother Tory leader because of this.
I also doubt that Barnier is willing to split out any of the Four Freedoms, but. Corbyn-led UK government could have a different interpretation of how to implement them.
For d), is there any expectation that it would go any differently if a different party were in power?