David Cameron's government is the biggest for more than a century, when reliable records began, despite the coalition's drastic reductions to the size of the civil service and public sector.

Figures from the House of Commons library show the prime minister's September reshuffle increased the number of MPs and peers serving in government to 121. There are also at least 43 MPs holding the post of private parliamentary secretary (PPS), seen as the first rung on the ministerial ladder.

Further study by Democratic Audit, a research unit at Liverpool University, shows the current government is more bloated than when Margaret Thatcher came to power more than three decades ago and is bigger than any government dating back to 1900, when Lord Salisbury was the Conservative prime minister with just 60 MPs and peers on the ministerial roll call.

The shadow leader of the Commons, Angela Eagle, accused the government of "blatant hypocrisy" for attacking the size of the state and civil service while "ever expanding" its own number.

There is concern about the growing power of the executive government as more MPs are constrained from challenging policies because they rely on No 10's patronage for their positions and an increasing number of unelected peers take charge of decisions.

Peter Riddell, director of the Institute for Government, reiterated recommendations for a reduction in the number of government positions contained in a series of reports including those of the Conservatives' 1980 Norton commission and the Tory-led public administration select committee last year.

"Some of the rise can be explained by the existence of the coalition," said Riddell. "But, as the number of civil servants is pruned back dramatically, the number of ministers should, at least, be capped properly.

"The current statutory limit on the number of paid ministers in the Commons [109] should be reinforced by preventing the creation of unpaid ministers to get around the restriction. And the number of PPSs should be cut dramatically."

Stuart Wilks-Heeg, Democratic Audit's director, said: "It is difficult to see why the number of government posts continues to grow, particularly given devolution [of powers to Scotland, Wales and Northern Ireland] and the stated desire of successive UK administrations to move to smaller government."

The growing size of government is being criticised by some Conservative MPs, who believe it undermines their core belief in "small government".

Tory MP Douglas Carswell, who has written a book on the subject, said the still-rising number of ministers reflected the growing size and scope of government activities, which meant that the current government spent more per person than any in peacetime history.

"We have a 19th-century democracy trying to hold to account a 21st-century-size government, and it doesn't work," said Carswell.

A Cabinet Office spokesperson said the main reason for the growth was the coalition, adding: "Despite that, the government has taken significant action to cut the pay bill for ministers. In May 2010, all ministerial salaries were cut by 5% and frozen for the duration of the parliament. Changes have been made to ministerial pensions so that ministers contribute more but get no extra benefits."

The Commons library research shows there are 121 MPs and peers who are cabinet secretaries, ministers or in the whips office, three more than when the coalition was formed in 2010, following a gradual rise from 105 in 1979.

In addition, the number of PPSs has risen from 40 in 1983, the first year for which figures are given, to a peak of 58 under Labour's Tony Blair in 2001 and 46 after the general election. Press reports suggest the current figure is 43-46.

• This article was amended on 11 October 2012 to clarify that this is the biggest government since reliable records began.