A confident Mr Nuttall suggested Theresa May had failed on tackling radical Islam when Home Secretary and getting net migration figures down to the tens of thousands despite repeated Tory promises.
Mrs May hopes to secure a new trade agreement with the EU to avoid carrying out her threat to walk away and rely purely on WTO regulations.
Brexit talks will start after Mrs May triggers Article 50, which she has vowed to trigger by the end of March.
Paul Nuttall questions whether Theresa May can "walk the walk"
Let’s have this Brexit done, clean, finished before the next general election
Mr Nuttall said: “The one thing I will say, I’m not convinced by these transitional arrangements, which will only happen after May 2019.
“There’s no end date on them and I challenge the Prime Minister, let’s have this Brexit done, clean, finished before the next general election.
“The other thing I will say about Theresa May is that she’s always been very good at talking the talk, but when it comes to walking the walk it always fails.
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“Whether that’s tackling radical Islam as Home Secretary, or indeed getting immigration figures down to the tens of thousands, both which she promised to do and did absolutely nothing.”
The Ukip leader also criticised the government over foreign aid spending and argued more money should be spent on the NHS instead.
He said: "The foreign aid budget at the moment which is due to go up to £15billion by the end of this parliament is an absolute outrage.
Theresa May arrives at the BBC studios to be interviewed by Andrew Marr on Sunday
"I want to see British taxpayers’ money spent here in our country on our own people."
Mrs May revealed in a speech on Brexit last Tuesday that the UK would quit the single market when it leaves the European Union.
She has insisted she can get a good deal for Britain and was looking forward to "positive and optimistic" talks with European counterparts.
"We want to get that good deal and we expect to be able to get that good deal," she said last week.