Following the sacking of Pete Best, The Beatles were quick to recruit their new drummer.
Ringo Starr wasn't a stranger to the band, having stood in for them on several occasions in Hamburg and Liverpool, where he primarily played for Rory Storm and the Hurricanes.
Ringo first played on the same bill as The Beatles on 13 March 1959, on the opening night of the Morgue Skiffle Cellar in Liverpool. He was playing with Al Caldwell's Texans, and further down the bill were the Quarrymen. Caldwell later became Rory Storm; the Quarrymen, of course, were to become The Beatles.
On 18 August 1962, for the first time, The Beatles were officially John, Paul, George and Ringo. Following a two-hour rehearsal they played at the Hulme Hall in Birkenhead from 10pm. The occasion was the local horticultural society's 17 annual dance.
The capacity for Hulme Hall was 450 but, due to the popularity of The Beatles, it was unofficially enlarged to 500 when they performed. The other three dates they played at the venue were 7 July, and 6 and 27 October 1962.

Pete Best was fired on August 15th never to play with the Beatles again. The Beatles played the Majestic Ballroom on Friday, August 17th, 1962. They played with Faron and the Flamingoes and Carl Terry and the Cruisers.
Did Ringo play this date or did someone else sit in ?
Johnny Hutchinson of The Big Three.