First weather forecast offered in The Times (4/9/1860)

(Well, wiki says 1861.) And all thanks to Robert Fitzroy -- yes, the one who took Charles Darwin along as a travelling companion on the Beagle, and was Governor of New Zealand for a couple of years. By this time he was a Rear Admiral and a member of the Royal Society. in 1854 he was appointed "Meteorological Statist to the Board of Trade". He used the telegraph to collect weather reports from all over the country, and started producing what seem at first to have been just "reports" of what the weather had been the previous day in various places. It's not clear from either Crystal or Wiki exactly when the predictive element came in. When it did, the term "weather-cast" was sometimes used, but eventually Fitzroy's preference, "forecast", became standard.
https://en.wikipedia.org/wiki/Robert_FitzRoy