Britain has come under fire from a senior UK-based leader of the Muslim Brotherhood – under scrutiny in a controversial government review – for sending congratulations to Egypt's new president, Abdel Fatah al-Sisi, who led the coup that overthrew the Brotherhood's Mohamed Morsi last year.

Ibrahim Munir, head of the Islamist movement's international organisation, criticised comments by the foreign secretary, William Hague, after Sisi's 96.1% victory was announced last week.

He said: "The results of the elections were false and the British government knows that. Congratulations reduce the diplomatic credibility of the British government by giving support to the military coup even after thousands of innocent protesters were killed."

Sisi's inauguration on Sunday was marked by an impromptu public holiday in Egypt. But the US and EU governments sent only low-level officials to the Cairo ceremony in a sign of their reservations about human rights abuses, mass trials and repression that includes the proscription of the Brotherhood as a terrorist organisation.

Britain was represented by its acting ambassador. Hague also called on Sisi "to implement the rights contained in the constitution".

After a brief ceremony, Sisi became president with the words: "I swear by God to protect the republican system, to respect the constitution and the law, to safeguard the people's interests, and to preserve the independence of the nation and the unity of its lands."

Munir, who was first imprisoned under Egypt's autocratic president Gamal Abdel Nasser in the 1950s, insisted the Brotherhood was cooperating fully with a government review of the Brotherhood ordered by David Cameron in April. The prime minister has been criticised for bowing to pressure from Saudi Arabia, the UAE and Egypt, all rattled by the role of Islamist movements in the Arab spring.

"The surprise is that there was connection between the Egyptian coup and the review," he said. "It came while peaceful protesters were being killed. It was also surprising because the British government already knows a lot about the Brotherhood. It knows that we respect the law."

Munir is to meet the review's author, Sir John Jenkins, the British ambassador to Saudi Arabia, this month. Jenkins has been touring Arab capitals meeting Brotherhood leaders all the while officials insist that his findings will reflect UK, not Saudi, views of the movement.

Munir denied that any meeting of senior Brotherhood leaders had taken place in the UK, contradicting suggestions that it was official ignorance of such an event that led Cameron to order the review in March.

"No high-profile meeting happened here last year," he said. "Our policy, especially in time of crisis, is that we don't hide anything. No one can imagine that the British government is unaware of who enters the country. This whole review is based on completely false information, and that is problematic." MI5 and MI6 have been asked to submit evidence, including an assessment of a deadly bus bombing in Sinai in February – which was condemned by the Brotherhood.

Charles Farr, head of the office for security and counter-terrorism at the Home Office, is also involved in the domestic aspects of the review. Requests for asylum from Egyptians are understood to have increased since the 2013 coup.

Academics have also been asked for their views, though many are sceptical. "It is a ridiculous exercise," said one. "They already know the Brotherhood inside out. They've been in the UK for years. This is all about pressure from the Saudis and others. Now they have to come up with a review, but there will be an outcry if anything comes out of it." Shadi Hamid, an authority on Islamist politics at the Brookings Institution, a US think tank, described the review as "dubious and transparently political". Other critics have warned of a "dangerous precedent" and fretted that it might "represent a risk to civil liberties and further erode human rights standards".

Munir said there was concern that the government might face financial pressure over the findings from the UAE and other Gulf states that are lucrative markets for the UK.

"Regardless of the outcome of the review, we will adhere to our principles – and the main one is acting peacefully," he added. "We will abide by British law, but history will judge this action. I expect this review will clear the name of the Brotherhood. But if the result is negative, we will deal with it legally."

The Brotherhood is being advised by Sir Ken Macdonald, a former director of public prosecutions. Munir is also a member of the Egyptian Muslim Brotherhood's leadership guidance bureau, most of whose other members are in prison or in hiding.