Chris Paton blogs that "the Irish Government has funded a new online database of interest to those with architects in their ancestry. The Dictionary of Irish Architects 1720-1940 at www.dia.ie can be searched by the name of the architect in question, or by the work he created."
Chris also mentions that Scottish architects can be researched online, at www.scottisharchitects.org.uk, which covers 1840-1980.
There does not seem to be an equivalent site for English or Welsh architects. There is some limited information at www.lookingatbuildings.org which serves as "an introduction to architecture with pages on Building Types, architectural styles and traditions and building materials and methods of construction, and an expanding guide and introduction to buildings in seven of England's cities. Research tools including glossary, links, an index of architects and their works and a guide to further reading on all aspects of English architecture."