The idea
It's great the institutions such as the Science Museum are free to enter, but it's clear that they could do with more funding (or less taxpayer input). So why not allow all UK taxpayers or citizens enter free of charge upon presentation of suitable ID and place an entry charge on all others. It's common throughout the rest of the world, so why not here?
Why is it important?
It'll reduce taxpayer support and hopefully give the museums extra revenue.