Science Fantasy, which also appeared under the titles Impulse and SF Impulse, was a British fantasy and science fiction magazine, launched in 1950 by Nova Publications as a companion to Nova's New Worlds. Walter Gillings was editor for the first two issues, and was then replaced by John Carnell, the editor of New Worlds, as a cost-saving measure. Carnell edited both magazines until Nova went out of business in early 1964. The titles were acquired by Roberts & Vinter, who hired Kyril Bonfiglioli to edit Science Fantasy; Bonfiglioli changed the title to Impulse in early 1966, but the new title led to confusion with the distributors and sales fell, though the magazine remained profitable. The title was changed again to SF Impulse for the last few issues. Science Fantasy ceased publication the following year, when Roberts & Vinter came under financial pressure after their printer went bankrupt.

Gillings had an inventory of material that he had acquired while editing Fantasy, and he drew on this for Science Fantasy, as well as incorporating his own fanzine, Science Fantasy Review, into the new magazine. Once Carnell took over, Science Fantasy typically ran a long lead novelette along with several shorter stories; prominent contributors in the 1950s included John Brunner, Ken Bulmer, and Brian Aldiss, whose first novel Nonstop appeared (in an early version) in the February 1956 issue. Fantasy stories began to appear more frequently during the latter half of the 1950s, and in the early 1960s Carnell began to publish Thomas Burnett Swann's well-received historical fantasies. Carnell felt that the literary quality of Science Fantasy was always higher than that of New Worlds, and in the early 1960s his efforts were rewarded with three consecutive Hugo nominations for best magazine. Under Bonfiglioli more new writers appeared, including Keith Roberts, Brian Stableford and Josephine Saxton. In the opinion of science fiction historian Mike Ashley, the final year of Impulse, as it was titled by that time, included some of the best material ever published in a British science fiction magazine.

In early 1946, John Carnell launched a new science fiction magazine titled New Worlds, published by Pendulum Publications. The first issue appeared in July 1946 and failed to sell well. The second issue, that October, sold better, but Pendulum went out of business before the end of 1947 with only one more issue released. A group of sf fans, including Carnell and Frank Cooper, decided to restart the magazine under their own control, and formed Nova Publications Ltd. The fourth issue appeared in April 1949.

At the same time that the first issue of New Worlds appeared, a separate British magazine called Fantasy was launched by Walter Gillings, a science fiction fan and a reporter by profession. Fantasy lasted for only three issues before closing in 1947, but Gillings had accumulated a substantial inventory of stories—enough to fill nine issues. Gillings followed the demise of Fantasy by publishing a fanzine, titled Fantasy Review, beginning in March 1947.

In 1950, with New Worlds on a stable quarterly schedule, Nova Publications decided to launch a companion, Science Fantasy. They chose Gillings as the editor, and his fanzine, which had been retitled Science Fantasy Review in 1949, was incorporated in the new magazine as a department. The first issue was dated Summer 1950, but printing disputes meant that the second issue was delayed until winter. Paper rationing delayed the third issue to Winter 1951, but before it appeared, Nova decided that it could no longer afford to have separate editors for New Worlds and Science Fantasy, and Gillings was let go. According to Carnell, there were also "fundamental differences of opinion" that led to the decision to replace him.

After the Spring 1953 issue, Nova Publications decided to switch printers, in order to cut costs and bring the cover price down from 2/- (10 p) to 1/6 (7.5 p). The new printers, The Carlton Press, failed to keep to the agreed printing schedule, and produced poor quality work; there were also printers' strikes, and this disruption caused extended delays in the appearance of the seventh issue. While the dispute with the printers was going on, Carnell and Maurice Goldsmith, a journalist acquaintance of Carnell's, put together a small conference of well-known science fiction authors, including Arthur C. Clarke and John Wyndham. Goldsmith covered the conference for Illustrated, a weekly magazine, and the article caught the attention of Maclaren & Sons Ltd, a technical trade publisher interested in launching a new sf magazine. Carnell turned down the offer because of his loyalty to Nova Publications, but subsequent discussions ultimately led to Maclaren taking control of Nova Publications, with a commitment to produce New Worlds on a monthly basis and Science Fantasy on a bimonthly schedule. Maclaren's legal department was helpful in resolving the dispute with The Carlton Press, and the seventh issue of Science Fantasy finally appeared with a cover date of March 1954.

In 1958, Nova decided to launch a British reprint of the American magazine Science Fiction Adventures, under the same title. The British Science Fiction Adventures lasted until May 1963, when it was felled by declining sales. New Worlds, Nova's flagship title, and Science Fantasy were also suffering from poor sales, with circulation estimated at about 5,000, though a change from bimonthly to a monthly schedule was also considered that year for Science Fantasy. In September Nova decided to close down both remaining titles, and in preparation for the change Carnell signed a contract in December 1963 to edit an original anthology series, New Writings in SF, for publisher Dennis Dobson. Readers' responses to news of the planned demise of the magazines included a letter from Michael Moorcock, published in the April 1964 New Worlds, asking how the British market would now be able to train writers to sell to the higher-paying US magazines.

In early 1964, David Warburton of Roberts & Vinter, an established publisher, heard from the printer of Science Fantasy and New Worlds that the magazines were going to fold shortly. Warburton decided that having a respectable magazine would help him in getting good distribution for Roberts & Vinter's books: Science Fantasy and New Worlds both had distribution arrangements with the two main British newsagents of the time, John Menzies and W.H. Smith. Carnell did not want to continue to edit the magazines in addition to New Writings in SF, and recommended Moorcock to Warburton; Kyril Bonfiglioli, an Oxford art dealer who was a friend of Brian Aldiss, also expressed an interest. Warburton gave Moorcock the choice of which magazine to edit; Moorcock chose New Worlds, and Bonfiglioli became the new editor of Science Fantasy. Roberts & Vinter changed the format from digest to paperback, and the first issue under Bonfiglioli's control was number 65, dated June–July 1964. The schedule was initially somewhat irregular, with each issue dated with two months even when two issues were only a month apart—for example, June–July 1964 was followed by July–August 1964. From March 1965 a regular monthly schedule was begun.