Public culture shouldn't be accessible to only those with means. Someone's country of origin has no bearing on that.

Half of the exhibits in these museums are of foreign origin as well, stolen during imperialism. So charging foreigners to see stolen items that could very well be from their own country is again ridiculous.

Thirdly, how many museums and art galleries have you been to that are clearly struggling for cash? I've been to many, and 9 times out of 10 they're in exquisite condition. Money isn't the fix for everything. Charging to enter museums could even backfire and result in a reduction in footfall and therefore donations.

I'm sure Baroness Margaret Hodge knows all about keeping culture afloat for the public good though and only has the public's best interests at heart...

The family moved to Orpington, Kent (present-day Greater London), where they started their family-owned steel-trading corporation, Stemcor.[7] It is now one of the world's largest privately held steel companies, with an annual turnover of over £6 billion in 2011.[8] Hodge is a major shareholder

She went on to study at the London School of Economics, graduating in 1966 with a third-class honours degree in government studies.[12] After working briefly on television political programmes, she began, but did not complete, a master's degree in philosophy at Bedford College, London.[13]

In 2015 there was considerable controversy about her benefiting, to the tune of £1.5 million, from assets repatriated from a Liechtenstein family trust in 2011 using the Liechtenstein disclosure facility, that reduced penalties and removed the risk of prosecution for Britons moving undeclared assets back to the UK. Coverage focused on the apparent hypocrisy in her condemnation of the use of tax havens.

https://en.wikipedia.org/wiki/Margaret_Hodge