I spent a bit of time looking and this paper is the closest I've found to an analysis on the subject - http://www.stm.unipi.it/Clioh/tabs/libri../2/05-Thane_53-82.pdf

edit - The article looks at whether or not achieving the vote actually gave women more power, beyond the abstract "we're allowed to have a voice" concept. It addresses the idea that once women got the vote, they weren't all that interested in it. The part that's relevant to this question looks at the 1918 vote and the one in 1922 (arguing that the 1918 vote, directly after women were given the right, is a poor representation because of its timing after WWI, and the short amount of time in order to register before the election). They look at 1922 newspaper articles which remark that a surprising number of women were at the polling stations, asking their own questions and making their own decisions, which the reporter says was not the case in 1918.

This is the most relevant section, on page 58:

The next general election, in 1922, was a more realistic test of the effects of the change in the franchise. On the day following the election, the Times, which had no obvious commitment to the cause of women, commented:

"The greatest surprise which those in charge of the polling booths had yesterday was the number of women who appeared to vote immediately after the booths were opened."

In 1918, wrote the reporter, women had been uncertain and diffident, "many of those who did vote were acconmpanied by men and their views were probably influenced by them." But:

"Yesterday the contrary was the case... canvassers found themselves questioned alertly and adroitly on matters not usually considered women's questions. Foreign policy was a strong point in moving women in constituencies. Women's questions as such played a small part in this election; women in many constituencies attended meetings especially called for them when they were held in private houses, but it may be doubted whether any candidate, woman or man, polled a large vote purely on his or her stand on these matters... in every constituency it was the big issues that counted and men's questions were undoubtedly also women's questions.

"So far from married women voting as their husbands told them to, it was quite evident that where there was influence, it was not necessarily wielded by the man... the percentage of women electors who voted may be taken as possibly greater than that of men and their vote must have influenced if it did not secure the election of the majority of candidates."