I have set the text to centre but this just keeps it where it is and moves the second line under the centre of the first. I want to centre the whole block but do not know how.

Try sticking this wherE you do your CSS overrides (eg Customizer):

blockquote {
display: block;
}

This will probably cause your citation to shift to the extreme right of the page. If you’d like to center this as well, add:

cite {
text-align:center;
}