The National Archives of Britain has released a new set of passenger manifests which cover British ports from 1890 to 1899 (with more lists to be added later — eventually the site will cover up to 1960.) You can search through the lists (and sign up for e-mail updates as more materials are added) at http://www.ancestorsonboard.com/ .
Search by first and last name, gender, origin or destination port. I did a search for Thomas Murphy. I got 55 results initially, though if I’d done a search for all name variants I would have gotten plenty more results. Search results are shown in a table that includes year of departure as well as destination and departure port.
That information is free. However if you want to view a transcript of the information or an image of the manifest itself, you’ll have to pay. Views/transcripts are purchased with “units”; 5 units to view a transcript and 30 units to view high-resolution color images of the manifests. This sounds like quite a bit until you see that you can buy 50 units for £5. If you purchase units here they’re also work on FindMyPast.com which also has similar genealogy/historical records.
More news and updates about the site at http://www.ancestorsonboard.com/getBlogContent.action .