the uk web archive is here:
previously to get your site added, you had to fill in a form to give permission.
I would think they would honour a removal request.
archive.org seems to not be really crawling regularly or very much,
robots directives (robots.txt, http header, html ) will stop webcrawlers.
It would be a nice feature of uk webarchive for the website operator that you could download the WARC (or other standard archive format) of the website snapshot.