London is pretty good for online baptism records - as long as the person was baptised in the Church of England (see especially the excellent London Metropolitan Archives collection on Ancestry, as well as e.g. Westminster Baptisms on Findmypast).
However not everyone was baptised, and if Peter had an Italian or otherwise southern European parent any baptism may well have been Catholic. I note that he didn’t marry in the Church of England (the marriage was in an Independent Chapel). His names Peter Paul Louis would have been an unusual combination in England at that time, but Pier Paolo is a well-used combination in Italy - Luigi is the Italian version of Louis.
There are some Catholic baptisms coming online (both Ancestry and Findmypast have some) but they are far less likely to have been digitised than Church of England ones, due in part to the historic reluctance of the Catholic church to make its registers available for digitisation. I would think it unlikely that many Catholic records survive from as early as the 1830s, when Catholics in England were only just getting used to the abolition of systemic discrimination against them by the Catholic Emancipation Act 1829. Worship is likely to have been mostly in ad hoc settings, rather than formal churches and chapels at that stage (though others will no doubt know more than I do about all of this - I am no expert on Catholic family history).
