London - Scottish First Minister Nicola Sturgeon warned on Monday she would not watch her country "driven off a hard Brexit cliff" as she voiced frustration at her latest talks with British Prime Minister Theresa May."Large parts of the meeting were deeply frustrating," she said after talks with May and the first ministers of the UK's other devolved administrations, Wales and Northern Ireland, in Downing Street."I don't know any more now about the UK government's approach to the EU negotiations than I did before I went in to the meeting," she told Sky News.The nationalist leader has threatened a second vote on independence for Scotland if it does not have continued access to Europe's single market after Britain leaves the European Union.Sturgeon said she would "try to be reasonable" but warned: "What I'm not prepared to do is to stand back and watch Scotland thrown off a hard Brexit cliff edge."May has promised EU leaders that she will start the formal negotiations on Brexit by the end of March, but has refused to set out her strategy beyond saying she would prioritise cutting immigration.There are fears that this would inevitably mean leaving the single market, a move opposed by businesses and the government in Scotland, where a majority voted in the June referendum to stay in the EU.Earlier, May's spokesperson said she was determined to secure a "united approach" to Brexit and rejected the idea of a separate arrangement for Scotland."A single UK position is vital to protect the UK's interests as a whole. We need to be sure we are not putting up barriers to trade within the UK," the spokesperson said.After Scottish ministers visited Brussels to try to secure support for their case, the spokesperson warned against working to "undermine" Britain's strategy.But Sturgeon retorted: "I can't undermine something that doesn't exist. It doesn't appear to me that there is a negotiating strategy."'Truly gigantic challenge' Welsh First Minister Carwyn Jones dismissed the idea of a separate deal for Scotland, but he is also pressing for continued access to the single market for all of the UK."The scale of the challenge is truly gigantic. Nobody has any details yet as to what happens next," he said.The first ministers are also pushing for each of the devolved parliaments to vote on the government's plans.May has refused to allow the British parliament a vote before she triggers Article 50 of the EU's Lisbon treaty, starting a two-year countdown to withdrawal.However, MPs are likely to vote on the final deal.In a statement after the two-hour meeting, May said: "The country is facing a negotiation of tremendous importance and it is imperative that the devolved administrations play their part in making it work."Monday's talks were also attended by First Minister Arlene Foster and Deputy First Minister Martin McGuinness, who share power in Northern Ireland.Many in the province - which like Scotland voted to stay in the EU, unlike England and Wales - fear the effect of Brexit on the fragile peace process, notably the introduction of a hard border with EU member Ireland.