A top political commentator has warned the prime minister he must “get a grip” in the rows over his chief of staff’s salary and donations he has accepted.

Political biographer and historian Sir Anthony Seldon said Sir Keir Starmer should either “get rid of Sue Gray or underpin her because he can’t let this carry on”.

Concerns over the power in government of Ms Gray, a former senior civil servant, emerged again this week when it was revealed she is paid more to be his chief of staff than the prime minister’s own salary of around £165,000.

And Sir Keir has also faced attacks over the number and value of freebies he has accepted, both in opposition and since winning the election.

He was given the use of a corporate box by Arsenal football club worth thousands of pounds, it has been reported.

Sir Anthony said the two issues revealed a “lack of grip” within the civil service that the prime minister should sort out, so that similar rows could be anticipated in future.

“You have to be extremely strong as number as prime minister, otherwise the anarchy happens that we now see, and it’s harder because he’s on the back foot,” he told BBC Radio 4.

Sir Keir had talked a lot about getting the standards regime sorted out, but he failed to, Sir Anthony said, adding: “This is noise that was so avoidable, and I think that speaks of A lack of grip within the whole Whitehall machine.”

“The prime minister can’t have this noise around them, so you have to spend some political capital sorting it out, whether that means that he gets rid of Sue Gray or underpins her – but he can’t let this carry on. He has to do one or the other and it will need to have somebody strong in there.”

The PM, a season-ticketholder and an avid supporter of the team, used the box for the first game of the season according to ITV News. Security fears prevent the prime minister from using his normal Arsenal seats.

The box is advertised as costing at least £8,750 per game.

The extent of donations accepted by Sir Keir has come under growing scrutiny this week after it emerged the prime minister – whose salary is – had initially failed to declare a donation for dresses for his wife, Victoria, from millionaire Labour peer Lord Waheed Alli.

Lord Alli bought more than £5,000 worth of clothes for Lady Victoria Starmer, and has given Sir Keir £18,685 of work clothes and several pairs of glasses.

It also emerged on Wednesday that Lady Starmer accepted two free tickets worth hundreds of pounds each to Taylor Swift’s Eras Tour.

Defending the prime minister, former shadow attorney general Emily Thornberry said: “These are things that happen all the time in politics,” questioning whether the public expected the prime minister to “take a packed lunch” to a state dinner at Buckingham Palace.

On Tuesday it was confirmed that Sir Keir will not face an investigation by the UK parliamentary watchdog – but questions have been raised over the number of freebies claimed by the prime minister.

The volume of gifts and hospitality donations accepted by Sir Keir while he was leader of the opposition has also raised eyebrows.

He received more than £70,000 worth of hospitality and gifts from UK sources over the last Parliament, including in June last year a private box for four at Epsom Downs Racecourse, with catering and tickets, worth £3,716, and four tickets to see Coldplay at the Etihad Stadium in Manchester worth £698.

He also received a number of individual tickets for football games, including four tickets with hospitality for Chelsea vs Arsenal valued at £1,650 and three tickets with hospitality for Crystal Palace vs Arsenal valued at £2,142.

When asked about donations in July, Sir Keir told reporters: “The system is one where if we take any contribution or donation of any sort that is all set out and declared. And that’s what we’ve done properly on my behalf.”

MPs must declare any gifts, benefits or hospitality with a value of over £300 that they receive from a UK source to the register of interests, which is updated fortnightly while Parliament is sitting.

They are expected to declare anything that might reasonably be thought by others to influence their actions or words as an MP.

The number of donations accepted by the Labour leader appears to be more than that accepted by previous leaders of the opposition.

David Cameron, who spent five years as the leader of the opposition, appeared to have accepted fewer donations of hospitality and gifts. While it is not directly comparable – as rules around declarations were tightened in 2010 – the overall volume of declarations was lower than that declared by Sir Keir as the leader of the opposition.

He accepted two tickets to the FA Cup Final at Wembley Stadium in May 2007, private plane and helicopter flights, as well as other gifts.

While Ed Miliband was Labour leader, he declared tickets to the paralympic games for himself and his wife of an unknown value, as well as upgrades on a British Airways flight to South Africa worth up to £5,866.

Jeremy Corbyn accepted tickets to Glastonbury worth around £450 two years in a row, but apart from that did not accept hospitality, aside from a book he donated to a museum.

Since stepping down as Labour leader, he has declared about £600,000 in donations to his legal fund.

Downing Street has been contacted for comment.