If the UK were to leave the EU, trade and travel across the English Channel might get trickier and there were also concerns that Brexit might disrupt the sensitive data traffic that formed an integral part of international businesses.
According to experts advising firms over costly changes, such as changing storage sites for customer data, re-routing flows for rewriting documentation, not much would change. In or out, UK companies would need to comply with the strict rules the EU imposed on anyone taking data from consumers in the bloc.
Also, concerns in Europe that the UK tolerated more intrusion by security agencies into privacy than, say, Germany, might mean a post-Brexit UK would continue facing demands from Brussels for even tighter guarantees for handling EU citizens' data, such as the US had been confronted with this year.
Much would depend on the manner in which the UK negotiated with what would now be a 27-nation EU after a Brexit, which would likely take effect some two years after the referendum on 23 June. Post Brexit, the UK would follow a pattern similar to that followed by other non-EU European countries.
Following Norway would mean that EU data regulations would continue to directly apply to the UK, while choosing the Swiss model, would give the UK, the freedom to choose its own data protection law - but firms trading with the EU would need to comply with the EU rules anyway.
Meanwhile, the campaign to take the UK out of the EU had opened up a remarkable 10-point lead over the Remain camp, according to an exclusive poll for The Independent.
The survey of 2,000 people by ORB found that 55 per cent believed the UK should leave the EU (up four points since our last poll in April), while 45 per cent wanted to remain in the EU (down four points). The figures also took into account, the likelihood of people to vote and was, by far, the biggest lead the Leave camp had enjoyed since ORB started polling the EU issue for The Independent a year ago, when it was Remain that enjoyed a 10-point lead. The figures had now turned.