Mr McDonnell played down suggestions from Emily Thornberry that Labour would "probably" support the deal obtained by Mrs May in a Commons vote this autumn, saying that the shadow foreign secretary was being "sarcastic".
The Opposition Labour party has said that it would not vote for the Brexit deal unless "the government are sensible and they negotiate properly. get a deal that meets the six tests".
Scottish National Party spokesman Michael Russell accused Mrs May of planning a "power grab" by repatriating some responsibilities now exercised in Brussels to Westminster rather than Edinburgh.
"Make no mistake, this government is absolutely committed to the devolution settlements as we have demonstrated beyond question with landmark pieces of legislation over the last few years".
May visited a parent-and-toddler group in the northeastern English city of Newcastle, met farmers near the Northern Irish town of Bangor, and she spoke to Welsh business representatives in the resort town of Barry - all on the same day.
Scotland and Wales are drawing up contingency plans to protect their own interests in case they can not reach agreement with May on how powers regained from Brussels are redistributed.
Interestingly, voters in Norwich were heavily in favour of remaining in the European Union, with 56.2pc voting this way, while Great Yarmouth had the highest proportion of leave votes with 71.5pc backing Brexit.
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And Theresa May's message is suitably upbeat.
Mrs May said she had an "absolute responsibility to protect the integrity of the United Kingdom as a whole" ahead of the trip.
"I am determined that as we leave the EU, and in the years ahead, we will strengthen the bonds that unite us, because ours is the world's most successful union".
Even so, ministers are still working overtime to convince the devolved administrations they won't lose out after Brexit.
Mrs May said: "I believe we can negotiate a good agreement which is tariff-free and as frictionless trade as possible, so we maintain those markets in the European Union, but also that we open up markets around the rest of the world".
But with obstacles like an elusive agreement on managing the border with Ireland, and tough talks on trade still ahead - and Parliament's final approval another potentially unsafe hazard for the government - the route to Britain's final exit still looks, in many respects, far less predictable and well choreographed than Mrs May's rapid journey today.
Most voters in England and Wales backed Brexit, while majorities in Scotland and Northern Ireland wanted the United Kingdom to stay in the EU. "No prime minister could leave these things to chance", she added.