The black-and-white pictures above are from Gaynor Williams. They show 'Rhyl Swimming Bath' otherwise known as Sussex Street Baths. This facility opened in 1905 for public bathing in tepid sea water. It was a small place with rather basic facilities and became less popular after the Open-Air Bathing Pool opened on the prom in 1930.
Sussex Street Baths closed in 1939 and the building was used as a storage place by the Army during WW2. After the war it reopened as an indoor market which eventually became known as The Old Market to distinguish it from the newer Queens Market across the road.
The colour photo was taken in 2009 by Yours Truly and shows the present use of the site: the shops Savers and Peacocks.
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MON 5th FEB 2018 UPDATE: Recently to hand is this postcard of a kind that is believed to have been sold to customers on the premises at Sussex Street Baths:
The postmark is indistinct but could be 1922. The illustration seems to me to be rather good. Sadly, the artist/cartoonist is not identified. The caption Alfred Huxley Walsall refers to the company that built the baths.
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SUN 8th APR 2018 UPDATE: Indoor baths had been quite a fad in Victorian times. A popular one in mid to late 1800s in Rhyl was Vaughan's at 15 High Street where a gent could get a haircut and shave as well as an invigorating dip in hot or cold water.
Presuming High Street has not been renumbered, Vaughan's was probably the rear part of the former Goldsmiths jewellers shop opposite McDonalds.
Another notable baths of the period was Astle's, Queen Street (now the Victory Club).
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