VS have a major issue looming, if Brexit goes the No Deal route. That is looking possible. Branson will have to buy back the AF/KL stake or cancel the deal to push VS back into the 50%+1 UK shareholding rules. This is apparently built into the AF agreement.
The other option is for DL to divest some shares and I can't see that happening.
I don't see any trouble linking Brexit (difficult and pinful as it is) and Virgin Atlantic shareholders. Right now VS is a British registered company, holding a UK aviation certificate. That won't change, Brexit, no Brexit, no-deal Brexit, soft Brexit or whatever.
After (allegedly) 30th March 2019 the EU-US Air Service Agreement will no longer cover UK airlines flying to the US, but i seems a new UK-US agreement in on its way and seems it'll be ready by that date.
Since VS does not fly a) within the EU, or b) from any point in the EU (outside UK) and the US, it seems it will suffice.
Under that new agreement any US airline could just shout "Virgin Atlantic is not really a UK airline" if and only if that future agreement defines some kind of minimum on how much British-owned has a British airline to be.
One quick solution should this problem arrise. One could see Delta buying 1% more of VS and as such, this movement will make VS overnight a suitable airline for flights between UK and US. It will just be a UK subsidiary of a US airline. Should the UK allow a British Airline to be +50% US-owned (plus 20% French) is debatable but workable.
It could rise some problems with 3rd countries, but..... being only 20% British owned right now, VS has not seen any.
If such a thing ever happens, there is an airline called Virgin Atlantic International Limited (VAIL) which is 100%-owned by VS and could adjust its shareholding pattern to match any desired criteria.