The Beatles recorded at least one - 'Baby, It's You', which appeared on their first album, 'Please Please Me'.
Gerry & the Pacemakers recorded at least two, 'Magic Moments' and 'The Story of My Life'.
The Searchers did at least one, 'This Empty Place'.
Billy J Kramer & The Dakotas did 'Trains, Boats and Planes'.
With the incredible output from Bacharach, along with Hal David on many songs between 1959 and the late '60s, it's inconceivable to think that at least a few more of the Liverpool-based acts didn't record at least one.