So farewell, Kevin Roberts. The Saatchi & Saatchi executive chairman resigned last week after giving an interview to Business Insider that was so riddled with sexism and complacency it is difficult to pick out a particular soundbite.

To summarise, Roberts said that there was no problem with sexual discrimination at Saatchi & Saatchi and that some women, and men, were looking just to be happy in life rather than climb up the ranks of a company. He also accused a female campaigner of “making up a lot of stuff to create a profile”.

Roberts was put on leave by Saatchi & Saatchi at the weekend before resigning on Wednesday, apologising for “my miscommunication on a number of points”.

This should not be the end of the matter, however. For a start, it was noticeable that Roberts apologised for “miscommunication” rather than the views that were expressed, while Saatchi & Saatchi also allowed him to resign rather than firing him, allowing the Lancastrian to protect what is left of his reputation.

But more importantly, chasing Roberts out of his job and celebrating his departure does not mean that all is well again in the advertising industry and beyond. To put it simply, all businesses are failing to put male and female workers on an equal footing. While some are heading in the right direction, there is so much more to do.

The Women’s Equality party in Britain wants quotas to be introduced so that 50% of a company’s board and 50% of its executive committee are made up of women within the next 10 years. It has also made proposals about how British companies can get there, including overhauling maternity and paternity policies so that there is shared parental leave of six weeks at 90% pay for both partners, and free childcare from nine months. Companies should also be forced to publish the average pay of male and female employees, and the gender balance at each level of management.

Despite the efforts of campaigners and the government-backed report by Lord Davies, the situation in Britain is shocking. Among leading companies there appears to be a mixture of those doing the minimum amount acceptable and those not bothering at all.

The Female FTSE Board Report, produced by Cranfield University, showed that less than 25% of boardroom recruits to FTSE 100 firms were female in the six months to March 2016, the lowest level since 2011.

This drop in recruitment is not because FTSE 100 boardrooms are overflowing with female voices. Just 26% of FTSE 100 directors are women – and the vast majority of these female directors are non-executives with no day-to-day power. When you just consider executive directors – such as chief executives or finance directors – the proportion falls to just 9.7%.

It is far easier for a company to increase its proportion of female directors by appointing an established businesswoman as a non-executive, rather than developing its own female employees and encouraging them through the ranks so they become executives.

Perhaps Roberts, who was also “head coach” for Saatchi & Saatchi’s parent, Publicis, should now be charged with helping firms elevate their female employees to the upper echelons of management? After all, he seems to understand their mindset.

On second thoughts, the Lancastrian should be left to enjoy holidays in his property in the Lake District. Britain has someone else far better placed to ensure gender equality in the boardroom and in business: Theresa May, the new prime minister. May has already spoken about tackling executive pay and corporate governance at Britain’s biggest companies. This must include dealing with the imbalance between men and women in the boardroom.

No one should celebrate Roberts’s departure from Saatchi & Saatchi. It does not solve anything. The important lesson from the saga must be that all businesses have a long way to go to improve the opportunities available for women – not that male executives should learn to keep their thoughts to themselves.

Rest of world shrugs off Brexit

These are early days in the post-referendum economy as far as solid data goes. Unsurprisingly then, commentators are divided over quite how serious the hit to demand and output has been. Surveys suggest confidence and activity tumbled in the wake of the vote to leave the EU, emboldening those who predicted a Brexit recession. Others, who think the UK can ride out this phase of uncertainty, say those early readings overplay firms’ and consumers’ kneejerk reactions to the vote.

That debate will rumble on for some time. But here is one prediction that has not yet come true: that a vote for Brexit would send shockwaves through the global economy.

So said the International Monetary Fund, so warned the Bank of England. Yet now it seems these observers fell into the trap of overestimating the UK’s role on the world stage. Global fallout from the vote has yet to transpire.

When it cut interest rates to a new record low last week, the Bank predicted the UK economy would suffer a sharp slowdown. As for global effects, there was less to be said: policymakers noted instead that there was “little evidence so far” of any “sizeable adverse economic impact”.

Business polls since the referendum signal a drop in output for the UK, but readings from equivalent surveys for the eurozone were little changed from before the historic vote. It is a similar story from the US, where the latest jobs report showed strong employment growth and a pick-up in earnings in July, putting an interest rate rise from the US Federal Reserve in play for as soon as September.

None of that is to say that a global economy that was febrile before the UK’s referendum is out of the woods. European banks, notably in Italy, still look vulnerable. China’s debt-fuelled economy continues its struggle to rebalance. The US faces its own uncertainties as the election nears.

Brexit contagion comes low down on this list of global risks. So far it seems the UK is taking the big hit. Britain voted to stand alone, and now it does.

Big money will be on small screens

Adults now spend an average of one day in seven online – a whole 25 hours a week. This year’s state of the nation report from telecoms watchdog Ofcom also finds that two-thirds of Britons credit the internet with inspiring them to try new things, such as recipes, restaurants, travel destinations and cultural events.

Google and Facebook may count their profits in multiples of billions but they are barely scratching the surface. Smartphones, the most widely owned internet device, are where the greatest advertising opportunity lies. The majority of laptops now use ad-blocking software, but commercial messaging is harder to shut out from smartphone social media apps, which people check between 10 and 50 times a day.

In the UK, the mobile ad market is worth £2.6bn, but the smallest screens account for just 30% of all spending on digital ads. Expect that balance to shift.