(Adds context, Scottish, Irish comment)
LONDON, March 4 (Reuters) - Prime Minister Theresa May defended her decision to rule out so-called 'passporting' rights for banks after Brexit, saying Britain could not become a "rule taker" when it came to financial services.
May said her vision for future ties to the EU was a credible one and she was confident of reaching a good Brexit deal, in an interview broadcast on Sunday but recorded on Friday after a speech in which she had appealed for more flexibility from the bloc.
Setting out her thinking in more detail, May said the financial services sector was too important to the British economy for Brussels to retain control of it under the existing 'passporting' arrangement.
Passporting rules allow EU finance companies to sell their services across the 28-member bloc with a local license, rather than getting a license to operate in each member country where it does business.
"If we were to accept 'passporting' we'd just be a rule taker, we'd have to abide by the rules that were being set elsewhere," May said in the interview with the BBC.
"Given the importance of financial stability, of ensuring the City of London, we can't just take the same rules without any say in them," May said.
The Confederation of British Industry lobby group said it was important to make sure alternative arrangements were put in place to prevent firms leaving London.
"Now we do have an opening negotiating position. It needs to be followed through, it needs to be followed through very quickly because financial services firms are moving now," CBI Director General Carolyn Fairbairn told BBC radio.
May wants financial services to be included in a free trade deal - something she believes it is still possible to achieve despite accusations from Brussels that her approach amounts to 'cherry picking' the best bits of the EU
"I've said before that no deal is better than a bad deal, but I'm confident that we can get a good deal, and get the right deal for the British people," May told the BBC.
"If we look at our future prosperity and security, in the UK and in the other 27 countries, actually the right deal for us will be the right deal for them too."
May's speech on Friday was broadly well received in Brussels and at home among the rival factions of her Conservative Party.
But, underlining the challenge May faces, Ireland's foreign minister Simon Coveney said on Sunday she still needed to spell out her approach to the Irish border - which will become the only land frontier between Britain and the EU after Brexit.
"She hasn't really gone into any more detail than we've already heard in terms of how she is going to solve the problem of maintaining a largely invisible border on the island of Ireland," Coveney told the BBC.
Scotland's first minister Nicola Sturgeon said she still hoped to build support for staying in the EU's single market and customs union - which May has ruled out.
Sturgeon said she was also was not ready to give Scotland's consent to legislation Britain must pass to formally end its EU membership.
"What she (May) was saying - and to give her some credit she was much more honest about this than we've heard from the government before - we're going to go through this very complicated, long, drawn out difficult process and end up worse off at the end of it," Scottish First Minister Nicola Sturgeon told ITV.
"Why would the first minister of Scotland, the first minister of Wales or anybody else who's interested in the long term prosperity of the country just accept that?" (Reporting by William James Editing by Alexander Smith and Andrew Heavens)