The content of Theresa May’s Brexit speech suggests she does not understand the full impact that leaving the customs union and single market will have, Ireland’s prime minister has warned.

Reacting to Ms May’s Mansion House speech on Friday evening Leo Varadkar said he was “concerned that some of the constraints” of the UK’s policy are “still not fully recognised” in Westminster.

The Taoiseach added that the UK needed to produce more “more detailed and realistic proposals” – which had been expected in today’s address – and that time was running out to do so.

In her speech the PM admitted for the first time that the UK would lose some trade access to its biggest market, but dug her heels in on the issue of the Irish border, where she suggested technology might help solve the problem.

She also warned the EU that refusing to include financial services in a Brexit trade deal would “hurt” its own economy and launched a defence of “cherry picking” areas of the single market.

“I welcome that she has given a number of important reassurances today, including restating her overall goal of a very close relationship with the EU,” Mr Varadkar said in a statement issued after the speech, citing Ms May’s “clear commitment to the Good Friday Agreement, the Northern Ireland peace process and the need to avoid a hard border” as positives.

But the Taoiseach added: “The speech included a number of signals about the type of future economic relationship that the UK Government wants. But it also recognised that the UK will face hard choices given constraints between some of the UK aims and the consequences of withdrawing from the European Union.

“For our part, a close economic relationship is very much in the interests of Irish business, as is a smooth transition period.

“However, I remain concerned that some of the constraints of leaving the Customs Union and the Single Market are still not fully recognised. We will now need to see more detailed and realistic proposals from the UK. Brexit is due to happen in a little over 12 months, so time is short.”

Ireland’s role in Brexit talks is crucial because of the issue of the Irish border, which has proved a sticking point in negotiations for months.

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Ireland’s foreign minister Simon Coveney said he welcomed Ms May’s “reiteration” of commitments made in December and that they “now need to be translated into concrete proposals on how a hard border can be avoided”.

The PM's speech has had a generally frosty reception in Brussels. Chief negotiator Michel Barnier said he welcomed it and and would take it into account when drawing up the EU's trade talks guidelines, but European Parliament Brexit chief accused the PM of relying on "vague aspirations".