The UK chart started on 14th November 1952 – first number one “Here in my heart” by Al Martino

In the 1950s it was not uncommon for different versions of a song by different singers would be about at the same time with more than one making the chart especially in the UK as there would often be British and American versions of a song.

On 6th November 1953 (almost a year after the chart was launched) the number one was “Answer Me” by David Whitfield
On 13th November 1953 it was the same song “Answer Me” sung by Frankie Laine
While Frankie Laine held the number one spot for 8 weeks, the 11th December 1953 was one of the rare occasions that 2 songs shared the number one spot – the other song was “Answer Me” by David Whitfield.

I believe that was the only time that the UK had the same song sharing the number 1 spot, however, there was another occasion where 2 versions of the same song had number one in consecutive weeks.
4th January 1957 the number one spot was “Singing the Blues” by Guy Mitchell
On 11th January 1957 it was “Singing the Blues” by Tommy Steele but only for one week as Guy Mitchell ‘s version was back at number 1 on the 18th January.

The first non-consecutive occurrence of the same song at number one in the UK charts by different Artists was in 1955
On 29th April 1955 the number one was “Cherry Pink and Apple Blossom White” by Perez ‘Prez’ Prado.
After 2 weeks at the top it was replaced by “Stranger in Paradise” by Tony Bennett for 2 weeks
And on 27th May 1955 number one was “Cherry Pink and Apple Blossom White” by Eddie Calvert