The 1929 United Kingdom General election was a close affair, with Labour winning a plurality of only 27 seats while actually losing the popular vote. A scan of the Constituency election results shows Labour beating the Conservatives by small margins (less than 2%) in fourteen seats and the Liberals beating them in a small margin in five seats. Flip these seats and you have a Conservative Plurality 281-273-54.
The first few months should function just as a continuation of the previous Baldwin government, but then comes the Great Depression. I'm guessing that with a narrow plurality, an attempt to form a coalition National Government will occur.