Thanks Chris, as Dazza said, you're right. You must remember that the 'gothick' kick off of Pugin et al was as a statemant against the percieved paganism of the neoclassical. Pugin himself didn't use the term gothic, he prefered to call it 'pointed' or 'christian'.
In a roundabout way, St Andrews church itself is a fantastic example of greek-revival favoured by Foster. Greek-revival was the later stage of neoclassical architecture and shows an increased influence of the greek ruins that where being explored for the first time by the west in the late 1700s.
The differences are subtle, but many. Compare
St Andrews (greek-revival) to
St Brides which is more standard neoclassical.