I am married to my wife who has dual UK and US citizenship. She has been told that because of her affiliations to the US (her US citizenship) she must close her stocks and shares ISA as the UK bank who is her broker is closing all accounts of people with any US connection. I have sole UK citizenship. Is there any tax reason why my wife could not gift me her capital and I pay it into my stocks and shares ISA and manage her investments for her. This obviously requires a great degree of trust, but apart from that is there any tax reason why I could/should not do this. I have spoken to my broker (same bank, same broker) who say they would not have a problem with that because as far as they are concerned the money would be coming from me. I obviously don't want to get into any legal hot water with either the US or UK tax authorities!
There is a warning flag I see on reading this - "I could... manage her investments for her". This implies that the mutual understanding between you two would be that she bears the 'beneficial interest' in the account, which is ultimately the same impact in terms of US reporting requirements that it seems your broker is trying to protect itself against. In general, a spouse making a gift to another individual may be allowed depending on the amount, but this wouldn't be a gift if she ultimately remains the beneficial holder.
As a side note, I will add that it is not clear from your answer whether your wife is currently meeting all reporting / filing requirements for US liabilities as a US citizen. You may want to research that issue further if you feel there is any risk she is not fully compliant.
I can't speak to the US tax liability, but holding someone else's investments in your ISA is a form of tax evasion - sheltering someone else's assets under your personal ISA allowance.
Of course if these are jointly owned assets, rather than transfering your wife's assets into your name, as your broker said there will be no UK problems.