Marriage licences (the alternative to having the banns called) were issued at a higher ecclesiastical level than the individual parish. The licences themselves almost never survive, but the allegation (the written undertaking that the parties were free to marry) was retained by the issuing authority. Searching for these can be complex, as there is no way of knowing who issued the licence. The LMA's research guide at http://www.cityoflondon.gov.uk/things-to-do/visiting-the-cit...
gives details of what is available and where.
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