That is really not the case in the private sector, especially the big consulting and FS firms who are big users of these rates (especially in London). It is seen as a security issue - they deliberately do not put the firm’s name on ID cards, as they are usually electronic access cards which could be lost or stolen. Similarly, corporate credit cards rarely have the firm’s name on them.

I have used heavily discounted corporate rates for many years all over London, and have not yet been asked for ID. If I was, all I could do would be to send an email from my work account which at least is clearly from the associated company.