Kingsboy48

I contacted the MP for my previous UK constituency regarding when and how I'd be able to vote in future UK elections now that the Elections Bill is law, this is his reply;

Thank you for getting in touch about the Elections Act and the widening of eligibility to vote in UK elections for overseas voters from the current 15 year limit. My team have checked the timings with the experts in the House of Commons Library who have answered as follows:
[...] The 15-year limit on overseas voter registration is to be removed and they will be able to register again in the constituency, having previously been registered to vote before they left.
However, they will not be able to register just yet.
Although the Elections Act has now been passed, the provisions in the Bill are being implemented in phases. The Government’s priority are the voter ID provisions for domestic voters in polling stations, and these will be in place in time for local elections in May 2023.
The new provisions for overseas voters need additional secondary legislation to be in place and this is expected next year. Once that is in place, newly enfranchised overseas voters will be able to register with the local council. It is expected this will be sometime later in 2023 or early 2024 but there is no firm date as yet.
So it is definitely on its way, but it hasn’t quite arrived yet! In the meantime, there’s some (rather more general) information about how to register as on overseas voter at https://www.gov.uk/voting-when-abroad but I’m sure this will be updated once your vote has been successfully restored!

Looks like I'll have to wait a while longer yet.