But that in cpnjunction with those 'we's, seem rather to indicate that Great Britain must lead the project. While it would clearly be out of bounds to include the US, USSR, and Commonwealth in the USE, that does not necessarily position the UK outside of it either.
Encouraging other countries to unite or form a union does not
imply that one intends to be one such united country or union.
For instance IIRC the UK supported a United Netherlands from outside.
If the UK was to say it was in favour of Korean unification,
that would not imply that the UK expected to be part of united Korea!
His speech does not consider the problem of how Britain could be a member
of two unions British Commonwealth and European Union with separate
geography, rules and circumstances, at the same time; such an omission
probably reflects that he did not aspire for GB/UK to be part of the USE.
Churchill also spoke in favour of other improbable unions,
union of France and Britain, union of Britain and USA.
But taking such rhetoric out of context is pointless.
This Leaver has not claimed Churchill as a Brexiter, and I don't think that the
Remainers can fairly claim Churchill as a supporter of an EU including the UK.