The belief in Brussels remains that, unless Mrs May blurs her red lines a lot more, she can not expect a trade deal that is significantly better than the EU's one with Canada, which covers most goods but barely any services, and which would imply a hard border in Ireland.
"What she (May) was saying - and to give her some credit she was much more honest about this than we've heard from the government before - we're going to go through this very complicated, long, drawn out hard process and end up worse off at the end of it", Scottish First Minister Nicola Sturgeon told ITV.
"What we do want to see are new customs arrangements, created to minimise any unnecessary costs or regulations at our borders so that trade can continue as frictionless as possible. So we need to strike a new balance".
Setting out her plans for the future partnership between the United Kingdom and the EU, May highlighted the need for ensuring a data protection deal is in place between the United Kingdom and the EU.
There was much anticipation of what tone the speech might take or what revelations might be contained therein, with the Financial Times' Sebastian Payne reporting that an "informed" Conservative MP had said May's speech could prove a "pill" for hard Brexiters to swallow, marking the end of the UK Government's "cake-and-eat-it" strategy.
As an Arctic blast swept Britain, the U.K. Prime Minister sent her warmest words yet to Brexit negotiators in Brussels.
Within an hour of Mrs May concluding her address, DUP leader Arlene Foster was welcoming the prime minister's remarks and especially the commitment not to "countenance any new border being created in the Irish Sea".
May said Britain and the EU would need an arrangement on data protection and it would have to be more than just an adequacy arrangement which is a status granted by the EU to countries outside the European Economic Area which provide a level of personal data protection that is "essentially equivalent" to that provided in European law.
"If this is cherry picking, then every trade arrangement is cherry picking", she told an audience of politicians and journalists at London's Mansion House.
The 61-year-old leader has long kept her cards to her chest, trying to avoid provoking those who want a clean break with the European Union, or others, who fear the world's sixth-largest economy will be hit if barriers are raised against a major trading partner.
"We must hope that they will be as positive and pragmatic as Theresa May".
Britain's opposition Labour party this week came out in favour of a new customs union, which is already backed by the main business lobby groups.
After Tánaiste Simon Coveney suggested the EU could block her plans to maintain a soft Irish border while leaving the customs union, Mr Lidington accepted it could be changed to accommodate concerns. Britain would follow the rules of the agencies and make a financial contribution for being part of them, May said.
Britain will make "binding commitments" to maintain some European Union regulations - potentially over state aid and competition rules - after Brexit.
"Yes, there will be ups and downs in the months ahead". She went on to tell the European Union it is time to "get on with it" while also hinting at her anger at threatened "walk outs" when talks get tough.
"By following the course I have set out today, I am confident we will get there and deliver the right outcome for Britain and the European Union".