Post-Brexit, could London become a separate kingdom within the United Kingdom?

The UK and its federated daughter states – former colonies such as Australia and Canada – may not be much different. Canada is a collection of independent provinces, each with its own powers, conjoined as a federation for shared purpose.

The UK is a united kingdom of different kingdoms.

With mechanisms, for centuries, to add or remove territories, change the laws, and change common custom.

Could some of the United Kingdom’s constituent kingdoms stay in the EU, and some parts leave, without damage to the unified UK?

Could the capital of England move back to Winchester? or go Birmingham? or to England’s geographic centre? Even as the Parliament of Great Britain and office of Prime Minister continues in London?

Precedents:

Images:

Coat of Arms of the London County Council: By Notscott ((Source: R. Crosley, London’s Coats of Arms (1928)) [Public domain], via Wikimedia Commons: https://commons.wikimedia.org/wiki/File%3ACountyLondon.svg
Seal of the Brussels Capital-Region: By SVG by SiBr4 [Public domain], via Wikimedia Commons: https://commons.wikimedia.org/wiki/File%3AFlag_of_the_Brussels-Capital_Region.svg
Seal of the District of Columbia: By District of Columbia – http://www.vectorslike.com/, Public Domain, https://commons.wikimedia.org/w/index.php?curid=32918640
Coat of Arms of Berlin: Ottfried Neubecker (1908–1992), [Public domain] via Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Coat_of_arms_of_Berlin.svg
Coat of Arms of Lübeck: By SVG by David Liuzzo [Public domain], via Wikimedia Commons: https://commons.wikimedia.org/wiki/File%3AWappen_L%C3%BCbeck_(Alt).svg