At first glance the newspaperarchive.com is a largely American audience aimed newspaper archive, but there are a surprising number of British titles in their archive. The site is a subscription based, but they do allow a number of preliminary views of the newspaper before insisting on the opening of a subscription.
What is interesting about this archive is that many of the titles have a very short run of dates. Perhaps one, two or three years. Newspapers and magazines which only lasted a short time and then finished, or just that the archive have access to a limited number. This, however, has an advantage as these smaller and short lived newspapers have not yet been archived on other newspaper archives.
There are also several newspaper titles published in Britain specifically with news from the colonies. For instance, the China Telegraph published bi-monthly on the arrival of mails from china, Japan, Siam, Java and Singapore. A potentially good resource for researching your ancestors if they travelled to the Far East.
When searching one carry narrow down to just British newspaper titles.