And did the Roman Catholic Church keep any proper records in that period?
By 18th century do you mean 1701-1799? Restrictions on Catholics in England began to be eased during the last third of the century and Catholic chapels were no longer illegal.
Some priests began keeping registers.
Burials may have been in Anglican churchyards unless there was a Catholic burial ground in an area.
Catholic Family History Society catholicfhs.online has published 2 booklets "Catholic Ancestors in London" volumes 1 & 2. Catholic FHS has a Facebook page.
Some early R.C. registers were transcribed and indexed in Catholic Record Society journals.
https://www.crs.org.uk See "Record Series" for individual issues. Some contain a miscellany of articles and register transcriptions so you may have to look at contents pages.
Embassies of Catholic countries had chapels in London.
Find My Past has R.C. registers from some dioceses.
If your Catholics were in London in 1767 they may have been included on the Returns of Papists that year. It was a census of Catholics, compiled by the Anglican curate of each parish. Returns made later in the century contain less information.
