Rosebrook,

Anything about the murder of Maria Martin would be topical, so a search through one of the online broadsheet collections might yield something. There's a link in the Mudcat Links section (in fact there's a few links there which might yield useful material for traditional English material from your period).
Otherwise there's some good Crimean War songs, but they're a decade and more later than your historical brief (but the rules cd be bent, surely).
Popular music of the day was pretty eclectic, so you'd get away with quite a lot of earlier 19th and later 18th century material - which is a much richer vein (all those ballad about Napoleon, Nelson,Wolfe etc). Nursery songs and rhymes should be fairly straightforwad, as they've hardly changed since then and long before.
There aren't so many lovesongs and tearjerkers that spring to mind - possibly because the fashion for the more maudlin and sentimental stuff came later in the Victorian era, but there should be plenty of stuff in the Digitrad which would fit the bill.
Try searching using the keywords - @ballad, @tearjerker, @british etc.
Much of the material from A.L.Loyd's Penguin collection of English Folk Songs, gathered as it was at the end of the 19th Century, was probably first learned by the singer's parents in the early 1840s, and there are plenty of good songs there - uploaded just a few weeks back. Try a forum search on Penguin (and I can guarantee you a few unexpected sniggers at some of the posts that come up!)

GW Good luck