While there was a vigil and rallies in London mourning Charlie Kirk and involving far-right groups, the claim that over a million British citizens gathered and that the event was explicitly 'against mass migration' and framed as 'make the UK great again' is not supported by the evidence.
Over a million British citizens are gathering in London to mourn Charlie Kirk, against mass migration and vowing to make the UK great again.

Thousands gather in London for far-right ‘unite the kingdom’ rally and counter-protest – UK politics live - Politics | The Guardian
Source: theguardian.com
Key Evidence
Vigils and rallies attracted hundreds to thousands of people, not over a million.
independent.co.ukindependent.co.ukCharlie Kirk shooting: Vigil to be held in London after political activist shot...
nbcnews.comnbcnews.comLondon braces for mass far-right rally where Charlie Kirk will be mourned+2 more
Charlie Kirk was a conservative activist with known views against mass migration and pro-Brexit.
express.co.ukexpress.co.ukCharlie Kirk's opinion on Brexit, immigration and Labour revealed
No sources mention the phrase 'make the UK great again' or an official anti-migration rally framing at these events (all sources).
Tributes focused on Kirk's character rather than specific political slogans.
dailymail.co.ukdailymail.co.ukCharlie Kirk's UK campaign group pays tribute to 'good Christian man who did not...
What the Evidence Shows
The sources confirm that Charlie Kirk, a prominent American conservative activist and Trump ally, was shot dead and that vigils and rallies were held in London to mourn him. Multiple reports describe hundreds to thousands of attendees gathering near the Montgomery Statue in Whitehall for vigils and far-right rallies. The Guardian mentions thousands attending a far-right 'unite the kingdom' rally with counter-protests, described as one of Britain's largest far-right rallies in decades. However, none of the sources provide evidence of attendance reaching over a million people. The numbers reported are in the hundreds or thousands range, which is typical for political rallies but far short of a million.independent.co.ukindependent.co.ukCharlie Kirk shooting: Vigil to be held in London after political activist shot...
nbcnews.comnbcnews.comLondon braces for mass far-right rally where Charlie Kirk will be mourned+3 more
Regarding the motivations, Charlie Kirk was known for his conservative views including opposition to mass migration and support for Brexit.express.co.ukexpress.co.ukCharlie Kirk's opinion on Brexit, immigration and Labour revealed The rallies included far-right elements who likely share anti-migration sentiments. However, no source explicitly states that the vigil or rally was officially framed as 'against mass migration' or used slogans like 'make the UK great again,' which is a phrase closely associated with Donald Trump’s US campaign rather than UK political movements. The tone of tributes emphasized Kirk as a 'good Christian man' rather than focusing on migration issues.
dailymail.co.ukdailymail.co.ukCharlie Kirk's UK campaign group pays tribute to 'good Christian man who did not...
In summary, while there was a significant gathering to mourn Charlie Kirk involving right-wing activists and some anti-migration sentiment may be inferred from his known positions, the scale of 'over a million' attendees and explicit rallying slogans as stated in the claim are not supported by available evidence.