Tim Barrow, the UK's permanent representative to the EU, informed the European Council of its intentions to invoke Article 50 next Wednesday.
While EU leaders will gather in April or May for a summit to agree on the "framework" for the Brexit talks, actual discussions with the United Kingdom can't begin until ministers from the 27 nations officially approve more-detailed negotiation directives to be drawn up by the Brussels-based European Commission.
IFG's research director, Dr Hannah White, told BBC Radio Four's Today programme: "The estimates we have heard are something between ten and 15 Bills required in the next two parliamentary sessions".
European Union leaders plan an initial response within two days of May triggering Article 50, before convening a summit in late April or early May to ratify guidelines for their chief Brexit negotiator, Michel Barnier.
Scotland and Northern Ireland voted to stay in the European Union in the Jun 23 referendum, while England and Wales voted to leave, resulting in a UK-wide vote of 52 per cent for Brexit.
London says the Brexit process is irreversible once Article 50 is triggered, although experts have said there is no legal ban on member states changing their minds before leaving the EU.
If all goes according to the two year negotiations set out in the official timetable, Brexit should happen in March 2019.
Draft deals - on the nature and relationship of Britain to the EU - will be hashed out, all requiring approval from at least 20 of the 27 EU countries and then ratification by the European Parliament.More news: Ryan Looks to Thursday Health Care Vote With More Elder Pay Help
He said: "I can only affect what I say, Theresa May can only affect what she says, and she can find herself in a position where she may get a better deal, from the European Union, A - If she asks for one in the first place, i.e. don't give up on being in the single market, and secondly if she doesn't practise gunboat diplomacy on her fellow Europeans".
Cash, a prominent Euroskeptic, said European Commission chief negotiator Michel Barnier's suggestion of a €60 billion divorce payment had been "fairly extravagant".
An EU spokesman said it was "ready and waiting" for the letter.
May's preparations were wrong-footed last week when Scottish First Minister Nicola Sturgeon, who opposes Brexit, announced plans to hold a new independence referendum in a bid to keep its European Union ties. "A deal that works for every nation and region of the United Kingdom and indeed for all of Europe - a new, positive partnership between the United Kingdom and our friends and allies in the European Union".
The view appeared to open up a split with David Jones, a minister in the Brexit department, who welcomed the "no exit fee" argument - first put forward in an explosive House of Lords report.
Opposition Labour leader Jeremy Corbyn said his party accepted the Prime Minister had a mandate to start the process of leaving the EU.
"We are on the threshold of the most important negotiation for this country for a generation".
The committee's report said: "If the Government continues to apply its anti-CJEU stance too rigidly it will severely limit its post-Brexit options for adequate alternative arrangements".