Not sure about 19th century, but there's a fairly well publicized accounts in 17th: for example the Sack of Baltimore (in Ireland) in 1631. One source: Des Ekin’s book "The Stolen Village: Baltimore and the Barbary Pirates". See also more related 17th century info here: http://www.bbc.co.uk/history/british/empire_seapower/white_slaves_01.shtml
I have a feeling that "up to 1830s" was likely Berwick mistaking the last recorded attack on the English (or neighbouring) soil for the 1830s end of the Tripoli based piracy on the sea.
One unattributed statement I was able to find was from "The Coming Of The Corsairs" article by David Stanton on Mudeford Sandbank News website (used to reside on http://www.msbnews.co.uk/pirates06.htm and can still be viewed on Wayback Machine)
Coast raids had become less common in the 18th century (the last recorded is in 1760)
I wasn't able to find an authoritative source on the amount of slaves, the furthest I managed to dig to was the following quote from Joshua London, the author of "Victory at Tripoli" book:
Contemporary scholars estimate that over 1 million white Christians from France and Italy to Spain, Holland, Great Britain, the Americas, and even Iceland were captured between 1500 and 1800.
An independent mention (again without authoritrative sourcing) is from the same "The Coming Of The Corsairs" article by David Stanton mentioned above:
The July 2000 Radio 4 documentary “Turks On The Coast” put the number of captives between 1600 and 1800 at over 100,000, but a more recent estimate by an American historian has put the number of Europeans enslaved 1530-1780 at 1.25 million.