One of the four inquiries into claims of a conflict of interest involving Boris Johnson and a US businesswoman has been scaled back and a second has been put on hold after requests by the police watchdog.

The Independent Office for Police Conduct (IOPC) is concerned that the reviews could prejudice its decision on whether to launch an investigation into allegations of misconduct in public office against Johnson when he was mayor of London.

The current mayor, Sadiq Khan, ordered an inquiry into his predecessor after it was reported that Johnson’s friend Jennifer Arcuri was awarded £126,000 in public money and given coveted places on mayoral trade missions despite failing to meet the criteria for them.

Khan’s officials appointed the London fire brigade general counsel, Kathryn Robinson, to look into London & Partners, the mayor’s promotional agency, which granted Arcuri £11,500 in sponsorship and a place on the trips after intervention from Johnson’s office.

Explaining Robinson’s investigation on LBC this month, Khan said it would look at three key questions: what processes were in place when Johnson was mayor, were those processes followed, and what lessons need to be learned.

Following a request by the IOPC, it has been decided Robinson will not examine Johnson’s time as mayor and will focus instead only on current procedures at L&P.

A separate review by City Hall’s watchdog has been paused following a similar request.

The IOPC is examining documents and emails handed over by L&P that relate to the sponsorship for Arcuri’s company and her places on trade trips, before it makes its decision about whether to investigate Johnson.

A spokesman for Khan said: “The mayor’s office has agreed with Kathryn Robinson that she will look into the processes currently in place at London & Partners and the Greater London Authority’s involvement in them, to see if they need to be strengthened. This review will begin shortly, irrespective of the IOPC’s work.”

He added: “The IOPC has informed GLA officers that they are concerned that unless the review is limited to current processes, there is a risk it could prejudice the work they are undertaking. Following completion of the IOPC’s processes, the review by Kathryn Robinson and the GLA oversight committee’s investigation, the mayor will consider whether any further steps are required.”

Robinson will review how L&P decides who goes on trade missions and how it sponsors external commercial events.

An official at the GLA formally referred the allegations to the IOPC last month because Johnson headed the mayor’s office for policing and crime as part of his role. The IOPC is expected to make a decision on whether to investigate by the end of October.

Separately, the IOPC has urged the London assembly’s oversight committee to pause its investigation into the allegations against Johnson.

A spokesman said: “The IOPC has a duty to seek to prevent prejudice to any criminal investigation and/or the administration of justice. Seeking evidence from persons who are likely to be witnesses or suspects in a potential criminal investigation carries a particularly high risk of prejudice because of the potential for contamination of their evidence, the risk of it being disclosed in public in a manner which may prejudice a trial and/or it becoming known to potential suspects in a manner which could permit obstruction of the investigation.”

The committee agreed on Wednesday to comply with the request, but its chair, the Labour assembly member Len Duvall, warned Johnson it would resume after the IOPC completes its investigation.

Speaking to the committee after it met in private to discuss the matter, Duvall said: “People are on notice that have already been contacted and we will advise others that we will resume our investigation once the IOPC has completed theirs.”

In a statement, he added: “The London assembly respects the IOPC’s remit and will not in any way interfere with its important work. However, the assembly also has an important role and special powers. We will consider using those powers immediately following the conclusion of the IOPC’s work.

“Subject to that important review by the IOPC, certain people should be on notice that the assembly may well be knocking on their door sometime soon.”

Last week, a letter from Johnson’s lawyers to the committee said it had no remit to investigate. The committee had threatened to use its powers to summon the former mayor to answer questions in person, as it did over his failed garden bridge project.

A fourth investigation is under way into how a £100,000 cyber skills immediate impact fund (CSIIF) grant aimed at fostering digital talent in the UK was awarded to Arcuri’s company, Hacker House.

On Wednesday, MPs will question the culture secretary, Nicky Morgan, about why her department awarded the money to the company despite its tenuous links to the UK.

Questions have already been raised in the Commons about the due diligence carried out on the grant approval after ministers justified awarding the money – meant to be spent on improving IT skills in the UK – by saying the company had a British phone number. Calls to the number from the Guardian were answered by a receptionist in the US, where Arcuri is now based.

In a letter to the committee, Morgan said “any notion of the prime minister influencing – whether directly or indirectly – any aspect of the due diligence, assessment and award of any grant funding made through the CSIIF is simply not true”.

Arcuri has denied she received any favouritism from Johnson, L&P or the government. The prime minister has insisted “full propriety” was followed and he has no interest to declare over Arcuri.