Ms Taylor heads a committee which is examining modernisation of the Commons and will meet for the first time tomorrow.
The existence of the shooting range is seen as one of the greatest anachronisms at Westminster, where many of the facilities for MPs and staff are poor.
However, while previous attempts to scrap it have been opposed by Conservative MPs, Labour's massive majorty is likely to doom it. And the lack of a creche at the Commons has long topped the list of complaints from women MPs, many of whom have spoken out against Westminster's "clubbish" male atmosphere.
The letter, which is supported by MPs from the last Parliament as well as the new intake, argues: "There are no childcare facilities, yet we still have room for a gun club. We are not interested in change for change's sake. However, we feel that this situation is anomalous and contradicts our aim to create a modern Parliamentary system which reflects the people's priorities."
One of the organisers of the letter, Lorna Fitzsimons, MP for Rochdale, said yesterday: "We have a historic chance to deliver a modern working parliamentary system that is appropriate for a thriving democracy. We have to be bold and talk not just about procedures. We have to lead by example.
"We cannot talk to employers and wring our hands about childcare facilities if we are not doing anything about it ourselves.
"It is totally inappropriate, if we are going to push through legislation against hand-gun ownership, to have a gun club."
Ruth Kelly, the new Labour MP for Bolton West, who last month gave birth to a son, is among those who has backed the calls for Commons child-minding facilities.
Another of the MPs who signed the letter, Yvette Cooper, MP for Pontefract and Castleford, said: "It is an inefficient use of space. What we need is a modern place in which to work and to do a good job for our constituents."
Because of the underground location of the shooting range it is unlikely to be suitable for a creche. Instead, the MPs propose that it should make way for office space which could, in turn, be converted into a childcare area.
Although the Government has been careful not to involve itself in a matter which is the responsibility of the House of Commons authorities, it is said to be supportive of modernising plans.