It depends whether you want a good school, or one that is socially smart with lots of middle-class families. Both the OLV schools (Wandsworth and Kensington) have the reputation of being quite posh, which you may find a good thing, or you may not.
There are loads of good catholic schools in north London, including Our Lady of Muswell, St Gilda's/St Peter in Chains in Crouch End, St Joan of Arc in Highbury, St John Evangelist near the Angel Islington, St Joseph's in Highgate. I don't really know about schools on the Hampstead side, but Rosary is meant to be good. Tbh most Catholic schools are pretty good, so I'd decide where you want to live first and work around that.
All of those schools have a very mixed intake though -- they're not like free private schools at all. The very sought-after secular schools will tend to have a more middle-class intake because they select on the basis of proximity, and schools in some areas may be surrounded almost entirely by houses in the £1M+ bracket. Catholic schools in central/north London will tend to have a good proportion of London irish families along with families from all over the world, with a particular predominance from West Africa, Poland, mediterranean Europe, South America and possibly Vietnam and the Philipines.
For catholic schools you don't need to live on the doorstep, it's usually done on priest's reference and whether you live within particular parish boundaries and/or attend a particular church. If your children are already school-age, then tbh it will depend on whether there are spaces in the relevant year groups. If you are applying for nursery/reception places, then download any forms beforehand and get your priest to fill them in and/or write a supporting letter stating that you attended mass in the parish where you live etc.