'banking and financial sector' is the standard English phrase (plural form 'banking and financial sectors' is less usual)

'banking and finance sector' is used in UK English

'banking and financial services' is also used, but in this context is more likely to be the name of the act (along the lines of the 'Financial Services Act 1986' [http://www.opsi.gov.uk/ACTS/acts2000/ukpga_20000008_en_1]), 'A Government Act introduced primarily to provide increased protection for investors and to regulate investment business' (http://www.finance-glossary.com/terms/Financial-Services-Act... which sounds as if it tallies with what you are working on.

Hence it would be reasonable to write something along the lines of the 'Banking and Financial Services Act [appropriate year]' that will introduce 'revised regulations for the banking and financial sector'.

Individual companies and institutions are usually referred to by type (viz merchant bank, investment bank, private bank, the various kinds of institutional investor such as pension funds and unit trusts, etc etc etc) or grouped as 'banks' or 'financial institutions'. Rarely 'a financial business' or 'a banking business'.

Apologies for URLs in text - I haven't worked out how to conjure up more web reference boxes.

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Note added at 20 hrs (2008-11-01 13:17:01 GMT)
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True, 'sector' will not take you direct to 'rörelse' , but 'banking' will (to 'bankrörelse'), and 'financial sector' is the standard plural for all the different entities involved in financial services, while 'financing businesses' isn't.
Further, quite apart from the plural problem, 'businesses' is problematic because the legislation governing financial services invariably (and in this case too?) covers 'non-commercial entities' or 'pools of assets' such as pension funds which aren't businesses but are 'rörelse'.
If you google the different variants as entire quotes, the differences in use appear - eg 'financial sector' on its own gets 4.9 million hits, 'banking and financial sector' gets over 200,000 hits, while 'financing businesses' where financing is a gerund (noun) rather than a verb drew a blank.