Then they’re probably DUKE OF YORK and PRINCE OF WALES.
The article mentions the Duke of York and Prince of Wales as already laid down (towards the end) so that's not them. Makes me wonder which ships these are now.
At this point, it was already too late for the funding described in this article to do any good - Germany would invade Poland on September 1st [eight and a half months after this article was written], and the USSR would follow Germany into Poland two weeks later.
For the record, these are the Wikipedia dates for Wales & York:
HMS Prince of WalesNote that even with what must have been the furious & frenetic activity at the beginning of the war, it still took about five years to complete both York & Wales [and even then, it looks as though Wales was rushed into service about six weeks early].
http://en.wikipedia.org/wiki/HMS_Prince_of_Wales_(53)
Ordered: 29 July 1936
Laid down: 1 January 1937
Launched: 3 May 1939
Commissioned: 19 January 1941 (completed 31 March)HMS Duke of York
http://en.wikipedia.org/wiki/HMS_Duke_of_York_(17)
Ordered: 16 November 1936
Laid down: 5 May 1937
Launched: 28 February 1940
Commissioned: 4 November 1941
As for the ships imagined in this article - if their hulls had even been laid by the beginning of the war, it seems doubtful that those hulls would have escaped at least some Luftwaffe bombardment.
Point of this being that ol' Don Rumsfeld was right: You go to the war with the Navy you have, not the Navy you wished you had...