Select committees are not glamorous, but in terms of holding the government to account, they are more respectable than the media and more constructive than Her Majesty's opposition.

These cross-party, backbench MPs, are not part of the executive, and therefore cut through much of the political nonsense – party or otherwise – and conduct honest, diligent scrutiny of each government department.

The system works well and has been largely unchanged for decades.

Recent alterations to the machinery – such as the election of members (rather than appointment by whips) – show no sign of diminishing the most important and distinct cultural trait of commons select committees, namely that MPs leave party politics at the committee room door.

Select committee recommendations make a significant impact on the UK's policy landscape. The science and technology committee – my personal favourite – has in recent years provided crucial advice to government on science and abortion law, science policy, and science advice. It brought engineering out of the public affairs wilderness, put the critically important issue of geoengineering on the political map, and gave tactical clout to science advisers in government.

But some unnecessary flaws in the design of select committees make these successes and others more hard-fought than they needed to be, and continue to prevent potentially valuable recommendations from hitting their mark.

Three simple changes could make select committees much more effective:

Quality: Reduce the number of select committees

MPs who are part of the government, part of the opposition front bench, or who are whips, are not permitted (for obvious reasons) to sit on select committees. This means that there is roughly one select committee place per eligible MP. Consequently, serving on a select committee is a routine rather than a hard-fought honour, and attendance on committees is often low.

If the number of select committees were reduced, this would reduce the number of places and increase the competition for places. The departmental link would have to be broken, but broader remits with competent and fully attended committees would more than make up the difference. Places on committees would once again be competitive and the best people would sit on them.

Power: The power to call for real evidence

Select committees have the power to call people to appear as witnesses and for papers and records to be sent to the committee for scrutiny (rather like a court of law). There are two exceptions. One is the royal family, which is not relevant here. The second, which is extremely relevant, considering the role of select committees to scrutinise government, is government.

It seems incredible that select committees do not have the power to call ministers to appear before them, and that they do not have the power to demand to see government papers. I have observed select committees forced to resort to the Freedom of Information Act to get hold of government papers, and still be refused them. This is constitutional nonsense and should be corrected by parliament at the earliest opportunity.

Tools: Evidence checks

Most inquiries take the format of a committee deciding on a topic, putting out a call for evidence, cross-examining some witnesses – the last of whom are from government – and then writing a report with a bunch of recommendations. This works fine, but with one small flaw, and one more significant consequence.

The small flaw is that, because government gives oral evidence after everyone else, it has a strategic advantage: time. It is not uncommon, for example, for the government to get out ahead of a select committee report by taking action in an area in which a select committee will soon report, just so that they can say, "we are already doing that".

The significant consequence is that, in the plethora of submissions that select committees receive, the central notion of "evidence" often gets lost. Stakeholders argue their positions and the government argues theirs. Politics reigns and reason loses out.

While I was working for the science and technology select committee, I came up with an alternative model which the Committee dubbed the "evidence check". The process was to send a request to government asking two questions of each of 10 topics. The questions were: what is the policy? and, what is the evidence on which that policy is based? From the responses – which were published – we selected topics to pursue further.

This format had two powerful benefits. First, it meant that at the start of the process the government's position was out in the open. The government had no room to hide and no time to issue a distraction, and scrutiny was able to take its natural course.

Second, it forced a focus on tangible, testable evidence, and how such evidence was used in policy formulation. That kind of rigour is crucial for policy scrutiny.

It might seem that an emphasis on evidence is particularly relevant to a committee on science and technology. But in fact, evidence is, or should be, a crucial part of policy across all government departments. That is why every government department has a chief scientific adviser (except the Treasury, which will surely get one soon).

The "evidence check" approach is therefore wholly appropriate for every select committee and would increase their impact dramatically.

These three simple changes would make our parliamentary democracy much stronger. If we are serious about our elected representatives holding the government to account, they should have the tools to do so: high quality committees, with serious powers and sharp tools.

Dr Christopher Tyler is executive director of the University of Cambridge Centre for Science and Policy