I did find its planning documents (application 180410), which don't say (that I can find) who owns the site - so perhaps it is the council and they are not proud of themselves. There is a heritage statement from the applicants, and an assessment from the planners which sees no adverse issues. But then "heritage" consists only of what's got a listing, so the Three Guineas and a few things further away. However, the five public comments (one from the owners of Thames Tower) and the Conservation Area Appraisal Committee are all agin' it, the CAAC quite vehemently so.
The bit of the heritage statement that refers to visual impact in general, rather than listed stuff, reads:
4.10 While it is recognised that the proposed digital screen will be noticeable in views of the listed former Station building, its location has been well considered in this context. In this regard, the proposed screen will be positioned so that it reads against the backdrop of the circa 2014 footbridge addition at the western end of the station. This will ensure that the proposed screen will not impede the key views of the heritage asset from the western end of Blagrave Street looking northwest, in particular (Plate 1 and Plate 2). It is also important to note that the screen will be obscured in other views, such as that from the northern end of Station Road, given the presence of Thames House (Plate 3). To the southwest of the station the terrain falls away beyond the entrance to the 2014 footbridge addition (i.e. Station Hill), which combined with the orientation of the screen (facing southeast), will lessen its prominence when read against the listed former Station building.
That bit about "it reads against the backdrop of the circa 2014 footbridge addition at the western end of the station" is a bit cheeky, isn't it? Certainly if you look back at the council's plans for the "public realm", and some councillors' aspirations for a station building of quality, the thing just looks all wrong.
But what did the plans say it would look like? This is Maxx Media's picture in the planning statement that's closest to mine. From there, of course you can't see the station - I went forward to the corner of Thames Tower, where you first can, so the lamp post is in my picture.