For more than a decade I have been trying to find out the extent of Britain's involvement in kidnap and torture after 9/11. The UK facilitated it, but by how much is not known. Complicity in torture is not just unacceptable in principle. It undermines the values that democracies seek to export.

What's more, as many leading experts in the security field have frequently pointed out, in the long run it makes the collection of intelligence more difficult – both at home and abroad – from those very communities whose cooperation we most need. An investigation is therefore as morally essential as it is expedient on security grounds. It is why the allegations of complicity in torture should concern the whole family of western democracies, as President Obama acknowledged on Friday.

Allegations and disclosures keep dribbling out – a recent example being the unsubstantiated claim that the US operated a black site on Diego Garcia with the UK's co-operation. Allegations like this need to be investigated. The worrying question is whether the will exists to do so.

There have already been two failed investigations into rendition. First, the Intelligence and Security Committee (ISC) failed to fulfil its oversight function, when its 2007 report on rendition, erroneously concluded that Britain was not complicit in rendition, only to be flatly contradicted by a High Court ruling in the Binyam Mohamed case the following year. In 2010, the Prime Minister courageously decided to hold an independent, judge-led inquiry. This was a huge step forward. But the Gibson Inquiry fell short from the beginning. Among other things it adopted a narrow approach to its remit – ignoring detainee transfer in theatre – and appeared to adopt a passive approach to information gathering. And it left the last word on what could be published to the Cabinet Secretary.

The inquiry was initially delayed by the discovery, in September 2011, of documents appearing to implicate the British intelligence services in renditions to Libya. On the same grounds, in January 2012, it was closed down.

Two investigations have therefore failed to get to the truth. What's more, having failed once, the ISC has now been asked to try again. The early signs do not inspire confidence that it is a priority for them. This is a mistake. The trickle of allegations and revelations doesn't go away. Recent responses from the Foreign Office to one of my questions about Diego Garcia reflect this. A little history is needed. In 2007, the Government assured me that Diego Garcia had not been used in the rendition programme. The following year then foreign secretary David Miliband was forced to make a statement correcting this, admitting that two US rendition flights landed on the island in 2002, despite assurances to the contrary.

When, in 2008, I asked the Foreign Office for Diego Garcia flight records, I was told that a thorough review had been conducted and no such information had been found. Last month, when I asked again, I was told these records had, in fact, been kept but flight records from 2002 were "incomplete due to water damage". Just a week later, in a twist worthy of Yes Minister, the Foreign Office announced that "previously wet paper records have been dried out" and "no flight records have been lost as a result of the water damage". Contradictory answers to simple questions undermine public confidence.

Unfortunately, the long awaited publication of the US Senate Intelligence Committee report on the rendition programme will probably not set the record straight on the extent of Britain's involvement. In advanced democracies such as the US and the UK, which work more closely on security and intelligence issues than any other countries in the world, the truth usually comes to light sooner or later. But in this case, the control principle, which governs the relationship between intelligence agencies, whereby information shared between agencies cannot be disclosed without the consent of the provider of that information, may greatly inhibit the release of any new information on activities where the two countries' security services work together. Much of the material on the UK is therefore likely to have been redacted.

The ISC must show not just that it is up to the task, but that it will get on with it. It should make a start now, not in the next parliament. If it encounters obstacles, it should say what they are. If it is overworked, it should ask for more resources. Unlike the departmental select committees, it can do so.

Establishing the facts – both the extent and the limits of the UK's involvement – is overdue. It could turn out that most of our involvement has already surfaced or it could turn out that there is more to be discovered. We just don't know. In this case, sunlight really will be the best disinfectant. With the truth established, Britain can draw a line under these allegations and demonstrate that we abide by the values that we expect of others. In doing so, the public can have greater confidence that the government will not facilitate this sort of activity in the future.

Andrew Tyrie, Conservative MP, is founder and chairman of the Commons all-party group on rendition