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A UK TV program suggested that some of the chlorine in tap water can be removed if you fine spray it from your hose, such as with un upside down fine sprayer.

Is this true? How effective is it?

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Actually this is a very interesting suggestion and this advice may have a very solid scientific basis. I had heard a related talk a couple of years ago on water mists generating hydrogen peroxide but the authors were quite reluctant to publish this observation because of a lack of a suitable explanation. The idea is very neat. If we spray a fine mist of pure water, a measurable quantity of hydrogen peroxide is immediately form in that mist. In 2022, this report appeared in the Journal of the American Chemical Society. See Masoud A. Mehrgardi, Mohammad Mofidfar, and Richard N. Zare Sprayed Water Microdroplets Are Able to Generate Hydrogen Peroxide Spontaneously, J. Am. Chem. Soc. 2022, 144, 17, 7606–7609.

However, hydrogen peroxide is naturally found in rainwater and this is well known. Hydrogen peroxide and hypochlorite ions (dissolved chlorine) cannot co-exist even for a fraction of a second and thus this advice appears to be valid. Hydrogen peroxide is converted to water and aqueous hypochlorite to chloride. This chemistry is also well known.

As someone who is interested in chem. history, I feel that this could be a re-discovery and if we open 19th century voluminous works, this comment might be present! If anyone is aware of older works, please leave a comment.

AChem
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    I think it's much simpler than this - chlorine (and to a lesser extent related compounds such as chloramine) will evaporate out of water if it left to sit. Aquarists do this routinely. Misting (or boiling which is another common approach) speeds up this process substantially. – Andrew Jun 17 '22 at 15:46
  • Both effects could be working. It could be synergistic. We cannot stop one or the other at the same time. Removing of dissolved gas by bubbling helium in the solvent was also routinely done in HPLC systems. – AChem Jun 17 '22 at 16:26