"You just have to hope that they will accept things like your birth certificate etc. and - as the article says - two forms of non-photo ID instead."
If the Windrush "Scandal" has proven anything, it's that this assumption simply does not hold.
This is a solution looking for a problem. Voter error, whether fraudulent or otherwise, is effective nonexistent in the UK. You should treat any and all measures that restrict access to voting in the name of reducing fraud with the highest levels of suspicion.