What was the first Buddhist text to be translated into English? When was it translated and by whom? Was it reasonably available to those interested and did it have much of an impact within academic circles and perhaps to the wider culture?
Another early translator, Elizabeth Peabody, is incorrectly named the first translator of a Buddhist text. Nevertheless, she made the translation before T.W.R. Davids. She doesn't appear to have made a big impact:
In 1844 the magazine published Peabody's translation of a portion of the Lotus Sutra from French, which was the first English version of a Buddhist scripture. The publication ceased shortly thereafter in April 1844.
I would give this honorary title to Max Muller's translation of Dhammappada, first published in 1869, later included in Muller's Sacred Books of the East series published around 1880s.
Beside Dhammapada, the series included important suttas such as Setting the Wheel of Dhamma in Motion, Mahaparinibbana, and others, all of Sutta-Nipata, most of Vinaya, one of the earliest post-canonical texts Milinda-panha, a Chinese version of the Life of Buddha by Asvaghosa, and some of the most important Mahayana texts such as Heart Sutra and Lotus Sutra.
Arguably this was the most notable early publication of Buddhist texts into English.
It depends somewhat on what you mean by a Buddhist text. The book of “Barlaam and Josephat” is a famous Christian reworking of the life of the Buddha. It was translated from Latin to Middle English in the 15th century.
Sándor Csoma de Kőrös (Hungarian: Kőrösi Csoma Sándor) was a Hungarian-Szekler orientalist who went to Asia around 1820 looking for the ancestors of Hungarians, but ended up in Tibet instead. He is well known among Hungarians for his journey and for compiling the first Tibetan-English dictionary and grammar.
He spent considerable time in Tibet studying Tibetan and Buddhist philosophy between 1827-30. He was declared Boddhisatva in 1933 in Japan.
While I do not know if he translated Buddhist texts into English, it is plausible that he may have, as he immersed himself in Buddhism. Unfortunately it is unlikely that this will be easy to research on the internet, you may need to go to dusty old libraries to get definitive information ;-) Nevertheless, I thought that this was a good lead which is worth mentioning (since the dates are similar but a bit earlier than in the other answers).
Some of the earliest translations are covered in the Sacred Books of the East (Dhammapada by Max Müller based on a Latin translation by Viggo Fausböll and Sutta-Nipata by Viggo Fausböll) series by Max Müller in which some of the books are Buddhist books as per the Theravada tradition.