Apple boss Tim Cook has told Theresa May he is 'very optimistic' about the UK's future after Brexit.

Mr Cook met the Prime Minister at Downing Street this morning to discuss the company's plans to build a new UK headquarters at the redeveloped Battersea Power Station as proof of the company's support of the UK.

'We're doubling down on a huge headquarters in the Battersea area and we're leaving significant space there to expand,' Mr Cook said.

'We're a big believer in the UK - we think you'll be just fine. Yes, there will be bumps in the road along the way but the UK's going to be fine.'

Theresa May has hosted Apple chief executive Tim Cook, pictured in Downing Street today, at No 10 for private talks on her Brexit plans

Apple boss Tim Cook today visited a primary school in north London as part of his trip to the UK to discuss Brexit with Theresa May

Last year the iPhone maker revealed it would move 1,600 employees to the new campus in south London in 2021.

In a statement about the meeting, Apple said: 'Tim had a positive meeting with the Prime Minister today, discussing Apple's continued investment in the United Kingdom.

'We are proud that Apple's innovation and growth now supports nearly 300,000 jobs across the UK.'

The 56-year-old (centre) chatted to children at Woodberry Down Community Primary School

After the meeting Mr Cook visited a primary school in north London.

The 56-year-old chatted to children at Woodberry Down Community Primary School in Harringay, which is part of the New Wave Federation group of schools that have incorporated Apple's iPad and related software into lesson plans.

Its students learn basic coding through Apple's Swift Playgrounds software and work with the company's GarageBand music app as part of their lessons.

'Technology has moved on considerably,' Mr Cook said.

'It gets kids a lot more engaged because they're living in a digital world. We're all living in a digital world.

'This school has done an unbelievable job of integrating it.'

The school is part of the New Wave Federation group of schools that have incorporated Apple's iPad and related software into lesson plans

Students learn basic coding through Apple's Swift Playgrounds software and work with the company's GarageBand music app as part of their lessons

Mr Cook was photographed sweeping into Downing Street this morning and was said to have held 'positive and useful' talks with the PM.

Mrs May's 'global Britain' strategy was boosted last year by Apple's announcement it would set up a huge new headquarters in London at the redeveloped Battersea Power Station.

The lavish plans raised hopes Apple could abandon its base in Ireland and shift its European operations to Britain in what would be a huge coup for London - and the Treasury.

The iPhone and iPad developer was slapped with a vast bill by the European Commission after Brussels ruled against a low corporate tax deal agreed between Apple and Ireland last year.

Mr Cook said: 'Technology has moved on considerably. It gets kids a lot more engaged because they're living in a digital world. We're all living in a digital world'

Mr Cook, pictured leaving No 10 after his talks, was said to have held 'positive and useful' talks with the PM

Revealing details of the meeting, Mrs May's official spokesman said: 'It was a meeting with the Prime Minister.

'It was a very positive and useful discussion. You have seen Apple has made a recent announcement about investment in the UK.

'There was a conversation around that, the importance of Government and business on digital skills going forward which is going to be a huge part of the future industry.

'And touching on what the Prime Minister outlined in our plans for negotiating EU exit.

'It was a chance for her to reiterate and welcome Apple's investment in the UK.'

The spokesman would not comment on whether Donald Trump's immigration summary or how Mr Cook responded to the Brexit plans.

Apple announced in September it would create a new London headquarters inside the £9billion Battersea Power Station development for up to 3,000 staff.

The Grade II listed building on the Thames with its iconic towers is key a feature of south London's skyline. It is being refurbished by a Malaysian-led consortium.

Mr Cook and his team were pictured leaving Downing Street this morning following his talks with Mrs May

The tech giant will occupy six floors - about half a million square feet of office space - in the central boiler house of the former coal-fired power station.

Apple, which insists it pays all taxes due in Britain, will become the largest office tenant in the new-look Battersea Power Station development.

In 2015 it sparked fury after revealing that it paid only £11.8million in British corporation tax the previous year – despite raking in profits estimated at almost £2billion.

It will take up around 40 per cent of the office space and spreading staff across six floors and employees will be relocated from various London offices in 2021, Apple said.

Apple has around 1,400 office staff in London working across nine sites and another 1,100 working in its UK stores.

The redevelopment of Battersea Power Station, pictured in December, is one of the biggest building projects currently underway in the capital

Once complete, Apple will occupy six floors - about half a million square feet of office space - in the central boiler house of the former coal-fired power station. Pictured: Computer generated projection of the revamped Battersea

Announcing its plans last year, it added that it was a 'great opportunity to have its entire team working and collaborating in one location while supporting the renovation of a neighbourhood rich with history'.

Rob Tincknell, chief executive of Battersea Power Station Development Company, said: 'We are delighted that Apple has chosen to make Battersea Power Station its home in 2021.

'It is testament to our fantastic building and the wider regeneration of the 42-acre site which offers a carefully curated mix of homes, businesses and leisure amidst extraordinary open spaces and new transport links.

'It has always been our clear objective to create one of London's most thriving new communities and this commitment from Apple will undoubtedly help us achieve our goal.'