score:3
I'm guessing you are mis-understanding the definition of a "temporary visitor" in the sense that it is used on that website.
In order to receive a Drivers License or ID card in Texas, you must be a resident of the state, and must be able to prove that fact. The "Temporary" refers to the fact that you can be a resident of the state, but not a "permanent resident" - such as if you are in the country on a long-term work visa.
So yes, the UK does have something similar to what Texas has in that non-permanent residents can apply for an ID card/Drivers license - but no, you will not be able to receive one if you are visiting for a week.
Upvote:2
You cannot get any kind of UK ID card, as attempts to introduce ID cards in UK have been completely repelled by Identity Documents Act 2010.