By Huw Jones

LONDON, July 19 (Reuters) - Britain has kicked off a review of how regulation of finance could be improved after Brexit, saying it would not tweak the existing set-up of watchdogs introduced in the aftermath of the financial crisis a decade ago.

The European Union has been the source of financial rules in Britain for decades but that is due to end on Oct. 31.

"It is now right that we step back to look at how the system is working more widely, and what changes may be needed in the future to adapt to the UK's new position outside of the EU," John Glen, Britain's financial services minister, said in a statement on Friday.

Britain's Financial Conduct Authority (FCA), and parliament's Treasury Select Committee are also reviewing future regulation of finance, the economy's biggest tax generating industry.

After the financial crisis forced taxpayers to bail out banks, Britain scrapped the Financial Services Authority.

It was replaced with two new bodies, the FCA and the Bank of England's Prudential Regulation Authority. A new BoE committee was also created to spot broad risks and set the tone and direction for regulatory oversight.

"The government continues to believe that these institutional arrangements provide the most effective way of ensuring clear and robust regulatory focus," the finance ministry said in its consultation paper.

"As such, it does not expect to examine these arrangements as part of the Future Regulatory Framework review."

The review could be divisive as domestic lenders and insurers want to distance themselves from EU rules, while cross-border banks and asset managers want to stay plugged into international standards to ensure access to the bloc.

Backers of Brexit say it presents an opportunity to ditch EU red tape and promote the competitiveness of London as a global financial centre.

The ministry said a regulatory framework should "support the ability of UK financial services to compete in international markets, as well as ensuring that the UK is open and attractive to new and existing trading partners".

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The Bank of England repeated last week that UK banking rules after Brexit should remain as robust as they were now. The consultation paper says Britain's regulatory framework should deliver "robust regulatory standards and supervision".

Public consultation will close in October, and future phases will look at how the regulatory framework "needs to adapt" to Britain leaving the EU.

(Reporting by Huw Jones Editing by Edmund Blair)