Attorney General Geoffrey Cox said last-minute new agreements "reduce the risk" of Britain being "indefinitely and involuntarily" held in the so-called Irish border backstop.
However, "the legal risk remains unchanged" that Britain, without being able to prove bad faith on behalf of the European Union, would have no legal means of exiting the backstop without the agreement of Brussels.
Prime Minister Theresa May rushed to Strasbourg on Monday for last-minute talks with European Commission president Jean-Claude Juncker in a bid to salvage the Brexit deal, with British MPs set to vote Tuesday on whether to accept the withdrawal agreement.
The two sides then announced a three-part package of legally-binding changes to the old deal.
The backstop, designed to keep the land border between the UK and Ireland free-flowing after Brexit, would see Britain stick to EU trade arrangements unless a new trade deal is struck.
Britain could not unilaterally pull out -- something that caused Brexit-backing MPs to vote down the deal in January.
Cox gave his legal opinion on the new wording struck between May and Juncker -- which could be crucial in determining how Brexiteers vote later Tuesday.
Cox said he now considered that the legally-binding provisions of the new documents "reduce the risk that the United Kingdom could be indefinitely and involuntarily detained" within the backstop, "at least in so far as that situation had been brought about by the bad faith or want of best endeavours of the EU".
He said that if both parties were indeed sincere in their desire to reach an agreement, it was "highly unlikely" that a subsequent agreement that would avoid the backstop kicking in would not be concluded.
Cox said that was a "political judgement" but one he strongly thought was right to make.
But in the final part of his conclusion, Cox said that legal risks of Britain being stuck in the backstop remained.
"The legal risk remains unchanged that if through no such demonstrable failure of either party, but simply because of intractable differences, that situation does arise, the United Kingdom would have, at least while the fundamental circumstances remained the same, no internationally lawful means of exiting the protocol's arrangements, save by agreement," he said.