Most licences for marriages in London/Middlesex at this period were issued by the Archbishop of Canterbury or the Bishop of London. The Diocese of Winchester also issued licences for some London/Surrey parishes.
Allegations/bonds for Archbishop of Canterbury licences are held at Lambeth Palace Library, but they have been indexed online (FindMyPast), in two separate indexes – Vicar-General and Faculty Office. After finding the licence date from the index on FindMyPast, the easiest way to get a sight of the originals is:
(a) from the microfilms at the Society of Genealogists, London (instructions on FindMyPast), or
(b) from FamilySearch (but accessible only at a LDS Family History Center or affiliated library).
Allegations/bonds for licences issued by the Diocese of London and the Diocese of Winchester are generally at London Metropolitan Archives, and may be indexed on Ancestry, with some images (but these are incomplete).
If you post some names, someone may be able to help.