Being able to vote anywhere is not an option - it would required digital voting, which we do not want.[1]
Requirements for registration is just one way to make voting hard. Others include requirements that voters cast their vote where they have official address, if change of address is cumbersome or expensive.
The government simply needs to know where you live to send you a voting slip. This is necessary because there's no equivalent to a national number in the UK.
If you read the article you linked, you would see that the voting registration was deliberately made harder to prevent voter turnout. There's no such issue in the UK.
You fail to explain why young/poor people tend to not register to vote. It doesn't cost money, there's no limit on age, it simply asks for your address. How hard is that? I did it on my phone in literally two minutes a while ago.