I don't think that St George's Hanover Square was a Catholic church, although that doesn't mean that Catholics didn't marry there.
Records of Catholics in London dating from the 18th century are relatively rare. The Catholic Family History Society has produced transcriptions of the registers of the Neapolitan Chapel, the Imperial Chapel and the Venetian Chapel which all date from the 18th Century. These were all chapels attached to foreign embassies and therefore immune to Government action and all three were used by London Catholic families. However I can't see any references to any Foulser families in any of them.
The only central London Catholic chapel open and functioning during the time period in which you are interested would seem to have been the Mission at Lincoln's Inn Fields [SS Anselm & Cecilia] - which was under the protection of the Sardinian Embassy. This has also been transcribed, but the registers date from a latter date than the one you want, see:
http://www.parishregister.com/parish_shop/product_detail.asp?ID=3476&CatID=289However I think that baptisms from an earlier date for this chapel were transcribed by the Catholic Record Society and should be available at the Metropolitan Record Office, or possibly through inter-library loan. *
The basic problem is that for the time that you are looking at Catholics were considered to be of doubtful loyalty and open practice of their faith was, to all intents and purposes, illegal. In areas of the country which were far from the Government in London, such as Lancashire, there was a reasonable degree of toleration, but in London life for those of the Catholic faith was difficult. As there were no churches as such baptisms carried out by Catholic priests were recorded in his personal book, if they were recorded at all and consequently few, if any, survive.
Sorry to be so pessimistic,
jds1949
*UPDATE - you can download this volume free from:
http://ia301514.us.archive.org/2/items/publicationscath11unkwuoft/publicationscath11unkwuoft.pdf