Thank you for your replies.....it looks as though I might have to pay for some info from FindMyPast!. I've applied for Francis' death certificate - that might (?) add a little more.
I don't know what else might be on your to-do list, but please don't rush into spending money there on the basis of what I wrote above:
Only yesterday I read that FindMyPast have just added a collection of Roman Catholic records for the Diocese of Leeds.
Millipede's answer is actually far more useful:
A family tree has a baptism for Elizabeth Hawkins 25 Dec 1823 parents Francis & Mary
Catholic under "England & Wales non-conformist and non-parochial registers 1567-1936"
Leeds St Mary's Lady Lane (Catholic) 1780-1827 the record appears to come from
I haven't actually been able to see anything useful in FindMyPast's Leeds RC collection, as it seems that for some reason the St Mary's registers are in this separate collection at the National Archives. The collection is mostly protestant non-conformist registers, so I was rather surprised to see them there, but you can find the list for yourself in TNA's catalogue:
https://discovery.nationalarchives.gov.uk/results/r?_aq=leeds%20st%20mary&_cr=rg4&_dss=range&_ro=any&_st=adv(If that doesn't work, do an advanced search for Leeds St Mary in class RG4.)
These RG4 collections are available at FindMyPast, but they're at Ancestry and The Genealogist too, so if you have a sub at either of those you won't need FindMyPast as well. Building on what Trish posted, there may have been 6 children's baptisms at St Mary's; one of them had a different mother's name, but I suspect it's a clerical error.
Unfortunately I didn't find any burial record for Francis. The other site which is always worth looking at for Leeds records is Yorkshire Burials (free, but you need to register), but again, I couldn't see him.
