It always seems to me to be more difficult to think of names for my characters than virtually any other of their attributes. If you look online for any inspiration there are a large number of baby naming websites which handle Christian names and a few that give historic frequencies of names given at birth.
However, I’d not come across much in the way of surnames until I did a Google search and came up with a brilliant site which is apparently part of a website for women called So Feminine. http://surname.sofeminine.co.uk/w/surnames/uk.html
Why it’s located there among articles about fashion and understanding your man, I can’t really explain. However it allows searching for individual surnames and gives an approximate breakdown for most surnames of geographical distribution around the country — I found that my surname is the most popular in Oxfordshire. (Odd as I thought it was most common in Nottinghamshire, although it’s not the overall accuracy that I’m interested in here as much as just a list of names.)
There are also lists of the most popular surnames — 8,500 of them in order should you wish to plough through them all. http://surname.sofeminine.co.uk/w/surnames/most-common-surnames-in-great-britain.html
While naming characters can offer possibilities of investment with some sort of allusion and meaning, this list perhaps throws up a few random bit of inspiration?