Kemi Badenoch has claimed that the Conservatives are “coming back” after winning back Westminster and Wandsworth councils from Labour in London, despite her party suffering significant losses throughout England in Thursday’s elections.

The party also saw off a threat from Reform in Bexley. But the Tories suffered a series of losses in Essex, where Badenoch herself is an MP, losing 13 seats while Reform gained 52. They held on to Harlow, securing all 11 district council seats available.

In Havering, where the Conservatives had 14 councillors before the election, the party was wiped out. With Reform making up 39 of Havering’s 55 councillors, the Havering Residents’ Association was pushed into second place as the official opposition with 11 councillors, while Labour held on to two of four seats with three independents.

Reform also made gains at the Tories’ expense in Suffolk, winning eight of the 12 available county council seats, and in Brentwood and North East Lincolnshire. A further blow came in Hampshire, where the Conservatives lost control of the council for the first time since 1997. Pressure has also rained down from Farage’s party in Norfolk.

In Staffordshire, the Conservatives lost control of Newcastle-under-Lyme borough council, as Reform increased its number of seats from one to a majority of 27, while Badenoch’s party fell from 26 seats to 15.

Speaking to party activists in Westminster, Badenoch said that the local result was proof that “Conservatives are coming back” and said her party had achieved “great results”.

“We have done brilliantly in Westminster,” she said. “We have taken back Wandsworth. People said nobody even expected anything to happen in Wandsworth. Wandsworth is now under Conservative control.

“Look at Fareham, where Reform said they were going to be marching through. Conservative hold. We were told we were going to be wiped out in Bexley. What happened in Bexley? Conservative hold. And our councillors there have actually increased their majorities? The Conservatives are coming back.”

The Conservatives and Labour had both performed better in London than in the rest of the country, emphasising the unique political landscape in the capital, said Prof Tony Travers, a local government expert at the London School of Economics. “The Tories have done surprisingly well, hanging on to Bexley, winning back Westminster and becoming the biggest party in Wandsworth,” he said, adding that a relatively strong showing from Labour and the Liberal Democrats in the capital suggested London voters were looking for less radical change than in other places in the country.

The political analyst Peter Kellner, the former president of YouGov, said it might be more accurate to say the Conservatives had done better than in local elections last year, when they were defending 996 seats and lost 675, a loss rate of 68%. By early evening on Friday that rate had fallen to about 44%.

“The Conservatives are way behind Reform, but compared with last year this is not a disaster,” he said. “If you compare it to historical standards or when the Conservatives were in power, it’s awful – but compared with last year, they’re doing slightly better and Reform are doing slightly worse.”

Henry Hill, a political commentator and longtime Conservative party watcher, said there was a danger that big-ticket gains such as Westminster risked masking a deeper problem for the Conservatives. “It could have been worse, this isn’t as bad as last year – but that is a low benchmark,” he said. “The Conservatives are still going backwards at a time when the government is spectacularly unpopular and its councillor base is being eviscerated – that is a bad position for any political party to be in.”