I had no idea about that Elizabeth House plan and its potential affect on Westminster.
If people wanted to judge for themselves then you can view the proposals here
My own personal opinion is that this development has very limited/ no impact on the Westminster WHS. The taller of the proposed buildings will be roughly the same as the already existing Shell Centre
and would mostly be tucked behind it. It would perhaps be in the background of views of Big Ben from one corner of Parliament Square when the trees don't have leaves on them.
The positives will be that it redevelops a rather ugly stretch of buildings, will open up access to the London's busiest rail terminus and add an impressive piece of architecture that compliments the buildings around it on the south bank. Actually I rather like this building and in comparison to many that are being built further east around the Tower of London it is actually very much in tune with the local built environment.
But what do I know, I'm only a World Heritage enthusiast with a particular fondness for Westminster who happens to use the proposed site on a weekly basis and can see it from my office window, so I'm probably not well placed to judge.
I guess it will probably be added to the list in danger in that case :(