The website ukcharts.20m.com states that "Once upon a time, it was quite a spectacular occurrence for a single to go straight in at number one ... Nowadays, if a single doesn't enter at the top then it has virtually no chance of getting there at all."
UK Charts lists a total of 38 singles that went straight in at No. 1 between 1952 and 1994. There were apparently two in the 1950s: Al Martino's Here in My Heart (which entered at No. 1 by default because it was No. 1 in the first ever chart), and Elvis Presley's Jailhouse Rock. There were three in the 1960s: It's Now or Never by Elvis Presley (1960), The Young Ones by Cliff & the Shadows (1962) and Get Back by the Beatles (1969). There were four in the 1970s (all in 1973: three by Slade, plus I Love You Love Me Love by Gary Glitter), 14 in the 1980s (including four in 1989), and 15 between 1991 and 1994 (there were none in 1990, and only one in 1992).
It's important to remember that from 1960 onwards this is referring to the Record Retailer chart, which was launched in 1960 and has since evolved into The Official UK Charts Company Ltd. This is also the one that's used by the BBC. Before 1960, the definitive chart was the one published by the New Musical Express (NME); the NME continued to publish its own chart (and still does to this day). The UK Charts wewebsite lists eleven singles that went straight to No. 1 on the NME chart in the 1960s. Eight of them are by the Beatles (seven in a row, from I Want to Hold Your Hand to Day Tripper / We Can Work it Out, and All You Need is Love); the other three are My Old Man's a Dustman by Lonnie Donegan (1960), Surrender by Elvis Presley (1961) and Little Red Rooster by the Rolling Stones (1964).
UK Charts notes that "Number One singles debuting at the top became the norm from April 1995 onwards." It lists 17 exceptions to this norm, from 1994 to 2001 inclusive; the same page refers to things that happened in 2003, which suggests that these 17 were the only ones to reach No. 1 having entered the charts at a lower position, from 1994 until some time in 2003. Guinness's British Hit Singles & Albums lists no fewer than 254 singles that reached No. 1 in the UK from 1994 to 2003 inclusive; so I think we can infer that possibly as many as 237 of these went straight in at No. 1.
Footnote: I'm not sure exactly what the status of the UK Charts website is; it doesn't seem to have been updated since 2003, but it does seem to be very well–informed. I'm guessing that it was the official website of the UK charts up till then; there's now a much slicker, more professional site, entitled Official Charts. There is also a third resource, calling itself The Official UK Charts Company: STATS AND FACTS, which seems to go up to 2007. This is on a website called Internet Archive: Wayback Machine. My guess is that the Official Charts Company started at www.ukcharts.20m.com, moved to www.theofficialcharts.com in 2003, but still wasn't happy and launched www.officialcharts.com in 2007, archiving the previous site on the Wayback Machine archive site. For whatever reason, it seems to have left the original site where it was. But your guess is as good as mine; what I'm saying is that I haven't been able to find anything on either of the two later sites (or, indeed, anywhere else on the Web) about singles that went straight in at No. 1, but whatever its provenance, the UK Charts site seems to be quite well informed and I'm prepared to believe what it says.
© Haydn Thompson 2017