Find My Past UK has added a collection of baptism and burial records from 1538-1890 for the 'county' of Middlesex to its database.
Some 175,000 records are included (95,545 baptisms and 79,541 burials), and it's worth checking them out if your Irish ancestors may have been in the London area.
The County of Middlesex has a troubled history! Ringing London to the east, north and west, it has been continually encroached upon by the capital city so that what now might be called Inner London was historically in Middlesex. Think Bethnal Green, the heart of London's East End and about as Cockney as you can get; it was once an area of disease ridden slums and poverty, and a lot of Irish lived there alongside other immigrant workers and paupers (certainly rather more than lived in the toffs' houses in other parts of Inner London/Middlesex, that's for sure).
The historic county has since been engulfed by Greater London or absorbed into the neighbouring counties of Hertfordshire and Surrey.
You can download a pdf of the areas covered by the baptism records here, and of the areas covered by the burial records here.