Leicester University have quite a collection of historical directories (Kellys / Post Office) online available to download free and with no login
here
Only up to 1919 at the moment (possibly a 100 year rule on copyright?) - quite a few of these are the same pdf's as some people will sell on CDrom on e-bay and so on.
for example, is a small chunk of the entry for Brixton Road, 1904 - i snipped this bit for one of editor's threads with an old photo.
If you're London based, it's worth bearing in mind that chunks of what's now London were Essex, Middlesex, Surrey or Kent until 1965. London was also divided in to 'London' and 'London Suburbs' directories and the boundary varied a bit from one year to another, but suburbs is roughly middle of zone 2 outwards. (Brixton is mostly in the 'suburbs' one)
From memory (I've saved a few to hard drive) it's a bit trial and error getting the whole thing rather than single pages, and at about 100 MB a go, they take a while to download but can sometimes be handy
On a different tack,
Welcome to Arthur Lloyd.co.uk is good on music halls / theatres (UK wide)