VAT should only be charged for local services - the actualy transport should not be subject to VAT. Only for example, if they delivery to a storage somewhere in Switzerland and have to deliver from there. On that last inland-transport VAT would apply.
You shouldn't get charged VAT for removal to Switzerland. We didn't get charged VAT last May when we moved from England, with the exception of the removal insurance which is charged at UK VAT rate.
You shouldn't get charged VAT for removal to Switzerland.
Actually that is correct. If you pay in England, you should not get charged for any Swiss VAT at all - this charge is not being forwarded over borders, only local.