By Francesco Guarascio and Huw Jones

The European Union will propose a single report on stock market transactions as part of efforts to build a "truly integrated" capital market after Brexit, an EU document showed on Thursday.

The European Commission is working on the next phase in creating a capital markets union (CMU) to help companies raise more funds by issuing stocks and bonds as the economy recovers from COVID-19.

A "consolidated tape" that knits together upwards of 20 trading platforms across Europe is a longstanding ambition to replicate the efficiencies of the U.S. stock market.

It would give investors a snapshot of prices at which each stock is traded. Some stocks are traded on multiple platforms, making it harder to see if investors are getting the best deal.

"The Commission will propose the necessary legislative changes to support the establishment of an effective and comprehensive post-trade consolidated tape for equity and equity-like financial instruments by Q4 2021," the European Commission briefing document seen by Reuters said.

The need to bolster the capital market has been made more urgent by the departure of Britain, Europe's biggest financial centre, from the EU.

The "vast majority of member states" are still "strongly opposed" to centralising more supervisory powers in the bloc, the document said.

"We could emphasise the need to develop a single rule book that would seek the alignment of rules and limit national supervisory discretion in the post-Brexit and multi-entry EU," the document said.

The European Commission is due to set out its proposals to bolster CMU on September 23.

"It will also include a careful narrative on Brexit and the need for the EU to develop its own full-fledged, well-functioning and integrated market for capital," the document said.

"At the same time, the need for sovereignty would have to be carefully balanced against the imperative to promote an outward-looking EU Capital Market Union that would continue to be attractive to third-country investors."

There is no consensus so far on how far to reform securitisation. Other ideas include extending the exemption for EU-regulated mutual funds from investor disclosure rules until they have been reworked.

The EU executive will assess by early 2022 the feasibility of a pan-EU label for financial advisors, it said.

(Reporting by Huw Jones)