What was the Beatles' first UK number one song?

It depends which chart you look at. 'Please Please Me' was the Beatles first ever #1 on any chart, reaching the highest position on the UKs NME top 40 in February of 1963.
https://en.wikipedia.org/wiki/The_Beatles_discography#Singles
NOTE: Reached #1 on the UK's NME. 'Please Please Me' only got to number two on the BBC/Gallup chart, which is what Guinness uses. But on the NME chart it was listed as joint number one with Frank Ifield's 'The Wayward Wind'.

The single was released in the UK on 11 January 1963 and reached No. 1 on the New Musical Express and Melody Maker charts. However, it only reached No. 2 on the Record Retailer chart, which subsequently evolved into the UK Singles Chart. Because of this it was not included on the multi-million selling Beatles compilation

https://en.wikipedia.org/wiki/Please_Please_Me_(song)

'From Me To You' (1963). Source: Guinness British Hit Singles.

According to "The New Musical Express" chart it was the song "Please Please Me" that had climbed to the No. 1 rank by February 22nd in 1963

Consequently, there will always be much debate as to which record was actually The Beatles first number one, and quiz compilers and the like should avoid asking this question because of the ambiguity of the answer!
http://www.jpgr.co.uk/stats_no1_s.html

This weblink says "From Me To You" on 2nd May 1963.
http://www.onlineweb.com/theones/1960_1964.htm

"From Me To You"

https://en.wikipedia.org/wiki/List_of_number-one_singles_of_1963_(UK)

http://hubpages.com/hub/The-Beatles-Number-One-Hits