Pretty much none directly, presuming you’re talking about the North American Home Video Game Crash of 1983. These markets were very far apart from each other, though in the matter of shifting the power of computer game publishers to the fore there was to be a long term impact. In the UK there was a large financial barrier to buying into consoles, therefore it wasn’t a significant portion of the market that would arouse the gaming climate in England.

So there’s three crashes to talk about here. The Video Game Crash of 1983, the North American Home Computer Crash of 1984, and the British Computer Game Crash of 1984. The effect of the first one was shifting the focus of home console companies towards computers, most notably Activision. Activision was a very early player in the European computer game space. They set up a label called Electric Dreams to convert software from the American market to run on British systems, though they were never particularly successful. Splinters from Activision like Accolade also did a heavy amount of business with U.S Gold, who would again convert their software to systems like the ZX Spectrum.

The second of these crashes was marketplace downfall in North America which resulted from a lot of social factors as much as economic ones. Basically the C64 wiped out the market for home computers and therefore stunted the growth of the computer game marketplace. This would be a heavy burden for companies like Electronic Arts which avoided console games like the plague, but they were not aggressive about pushing into Europe at first (though they would be towards the early 90s).

Finally the British specific crash. A large amount of disorganization within the publishers, growing out of them being largely born from hobbyist ambitions, made their organizations fall apart pretty fast. The market for computer games was still growing, but they vastly overestimated how much they could sell because the boom took off so quickly. The story of Imagine Software is the posterchild for this disaster, having placed a large amount of investment on stunting another major problem: Piracy and commercial counterfeiting.

In Britain the software was largely distributed by cassette which made it very easy to copy. Capital prevented the average consumer from buying something truly state of the art to go with their already costly system computer so British publishers were always racing towards the bottom in terms of pricing. Imagine attempted to create games which were impressive and locked via hardware to prevent piracy, ending with the company going into total bankruptcy literally on television.

There are trickle-down effects of all of these crashes. Employees from Imagine form Psygnosis which would eventually create Wipeout, a huge part of increasing the Playstation’s appeal worldwide. The eventual revival of the American home console market gave room for Sega to breach into Europe and effectively dominate the UK. The shifting of computer game publishers onto consoles would be the model followed by Eidos, of course best known for Tomb Raider. As for a direct effect of the North American Video Game Crash of 1983 to radically changing things in Europe, that’s not the case. There were less games, but on systems nobody was buying anyways.

Sources:

The Story of U.S Gold by Chris Wilkins and Roger M Kean. One of the best “Britsoft” books out there. Gives you a very sharp look into the windows of the West-obsessed publisher which controlled a large portion of the British market in the late 1980s.

Replay: The History of Video Games by Tristan Donovan. An alternative overview to the above-linked posts by Jimmy Maher. Also covers the 1983 Crash in a bit more explicit detail than any other current monograph.

They Create Worlds: The British 8-Bit Computer Market: Software from Alex Smith. Alex has done more comprehensive looking into the British market than anyone I know. If you need specific sources about the claims in this episode, I can ask him.