It’s been a bruising first week back for the government, full of resignations, reshuffles, and ructions in markets.

All of this will have an impact on what ends up in the chancellor’s famous red box outside No 11 in 11 weeks’ time.

The first thing to note is that it will be Rachel Reeves holding that briefcase for the second time on 26 November.

Whatever occurred with the deputy prime minister, the security of Reeves’ position was apparent in her conversation with me in Birmingham to announce the date of the Budget.

In Downing Street, the message received from the market reaction to the chancellor’s summer tears in the Commons was that the cost of borrowing went up when it was thought she was leaving office.

When I saw her, brandishing a hard hat and trowel at a housebuilding site, there seemed no question of her going anywhere.

“We need you to get qualified and get more flats and houses up,” she told two bricklaying apprentices, while not entirely convincing with her own trowel technique.

She rather robustly dismissed speculation about Budget measures, large black hole forecasts, and had some sharpish words even for the Office for Budget Responsibility, which we will come back to.

The chancellor spent the summer travelling the country “listening to business” and taking some time off on the Cornish coast.

During that same period global bond markets have been looking fragile. Some economists have even floated the idea there is a £50bn black hole that could lead to the need for loans from the IMF.

As politicians returned to work this week, and US traders returned on Tuesday from a national holiday, the 30-year gilt rate – the effective interest rate facing the UK government for very long-term borrowing – was heading for highs not seen since the early days of Tony Blair and Gordon Brown.

There was some significance to the unwanted landmark: the gains from nearly three decades of relative macroeconomic stability since the Bank of England became independent were being unwound.

I put to the chancellor that fragile bond markets were a reflection of the government’s, and her own, personal credibility issue. I have had similar interactions with previous chancellors, including Kwasi Kwarteng.

Reeves was adamant that this was not the case, that the move in bond markets since the beginning of the year had been in line with global trends. “Serious economists” were not talking about the IMF or a UK-specific challenge, she said.

By the end of the week, her bullishness was being proven accurate. The 30-year yield had fallen back, not just to where it was on Monday, but significantly lower, mainly off the back of weaker-than-expected US jobs data.

This was in common with many major economies. In other words, this week’s bond markets rollercoaster was not a verdict on UK domestic, economic or political developments.

Indeed, by Wednesday the Bank of England governor Andrew Bailey was playing down the entire focus on this measure, saying, “It is quite a high number but it is not what is being used for funding at all at the moment actually.”

He was referring to the fact that such long-term borrowing only makes up a small fraction of overall government debt.

And in terms of demand, there was no sign of a lack of appetite in actual sales of UK debt last week, with record demand on some measures.

The bigger picture though is that these forms of debt do not directly affect, for example, five-year fixed mortgage rates.

So the gilt markets are not fundamentally showing a mini-budget style UK-specific problem. At the same time, there is a clear warning signal here.

Fragile global bond markets do keep an eye on any unattractive economic or political factors. In this case the UK’s high inflation, and any doubt after the summer U-turns about the government’s control over events, could quickly turn problematic.

Indeed, expect the chancellor’s team to use the bond market rollercoaster to make the case that the answer to the autumn’s tricky Budget balancing act is not more debt through watering down her borrowing limits. Any gap, they will argue, will have to be filled by higher taxes or lower spending.

The amount of that adjustment depends on markets and the judgement of the OBR on the long-term performance of the economy. There was some substance to the chancellor’s off-the-cuff comments to me suggesting the forecasters stick to their primary role rather than giving a “running commentary on policy”.

The OBR judgement on UK productivity could be the single biggest determinant of how much of a gap there is, and therefore how much Budget pain the chancellor needs to administer.

Expect some haggling, with the Downing Street team of economists adamant that the OBR’s forecast should reflect their reforms, especially on planning. The first take of that critical independent judgement is expected to be delivered to the chancellor in the final days of this month, around the time of her conference speech in Liverpool.

At that point the long list of potential Budget revenue raisers will start to populate the Treasury spreadsheet known as the “scorecard”. Rumours will fly around. Indeed ministers are amazed at some of the speculation so far. For example, bank shares fell on suggestions the chancellor would enact a think tank report on windfall taxes, published when she was on holiday, that she has never even read.

Departmental budgets have already been set in the Spending Review, and there is no plan to reopen that process, which must mean that any restraint will have to come from the wider Welfare Bill.

The chancellor did not rule that out to me, but said there was “more to do” on reforms that helped people back into work. The new cabinet, without the former deputy PM, author of a leaked letter on wealth taxes, might be more amenable.

All in all this is the chancellor’s chance to author some long-term, pro-growth reforms to the tax system. She still hopes to do that.

But OBR spreadsheets, market ructions, and backbench unhappiness on cuts will ultimately determine just how big the extra tax demand in the red box is on 26 November.

Much can change between now and then.