In many cases it is most useful to "work backward" when assembling provenance information -- start with the object itself and use the institutional files from the owning repository as the building blocks for your research.
Look closely at the front of the painting and record any inscriptions, signatures, dates or numbers that are visible. The back of the painting may contain stamps, stickers, seals, or labels – record all of the visual information and assess in conjunction with the institution’s object files. Curatorial files, Registrar’s files, Conservation files, and the Institutional Archives may all hold important provenance information-- purchase receipts, dealer correspondence, and donor information.
A detailed explanation of assembling information from the object and institutional files can be found in: The AAM Guide to Provenance Research by Nancy H. Yei, Konstantin Akinsha, and Amy L. Walsh, The American Association of Museums, c2001. p. 11-19.
To find objects that are in the Collection of the Yale Center for British Art you can access the collections search page at: http://britishart.yale.edu/collections/search.
Researchers can also search the collections of the Yale Art Gallery.
The British Museum has an extensive collection searchable online at: http://www.britishmuseum.org/research/collection_online/search.aspx