The rules regarding sickness are grey again, they say everyone has to produce a sickness note from the doctor and you will only receive SSP if off sick. If you are genuinely sick the company has no honour your contract which pays full salary when off sick and if they dont you may pursue this legally and probably with union assitance (if there was ever a reason to be a union member here is one) anyone genuinely falling sick is being persecuted. - you have done nothing wrong and are only off work due to sickness.
I suspect the company have no beef with anyone who is genuinely sick, but you cannot deny that large numbers of crew have been advocating calling in sick in order to either still receive payment when they are on strike, or just to semi-support the strike without the conviction to say so. Either way, those staff are technically in breech of their contract by striking, so Virgin does not have to honour sick pay policy. Indeed, there is criminal intent in obtaining money by deception, and that could be considered an act of gross misconduct; and you'd be out of the door without need for disciplinary procedures.
Now I understand that this will mean more rigourous checking of genuine cases, and it is normal for companies to cover the expense of a medical certificate if required under 7 days; but Virgin are within their right to protect their business, and don't doubt that they will be asking for proof if you are sick during the strike. You won't be able to hide behind technicalities in policy, but then if you are genuinely sick, you have nothing to worry about.
Whether the company is allowed to switch to SSP only, then, as you say, it's a bit of a grey area. No disrespect; but I suspect the (large) VS legal team have looked into this a little more carefully than the advice of your employment lawyer. If you want to fight the company for the difference between SSP and normal sick pay; good luck to you.