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* FTSE 100 down 0.6 pct
* Hargreaves Lansdown falls after FCA report
* Oil stocks, miners drag
* Bunzl bounces after update
LONDON, June 28 (Reuters) - Britain's top share index dipped on Wednesday following a slide in shares of Hargreaves Lansdown and oil firms, though a jump in Bunzl's shares offered some relief.
The blue chip FTSE 100 index had fallen 0.6 percent to 7,391.88 points by 0831 GMT, while British mid caps were also down 0.6 percent.
Fund platform Hargreaves Lansdown was the biggest faller, dropping around 3 percent and hitting a one-month low following an industry report by Britain's markets watchdog.
In a drive to improve funds transparency, the Financial Conduct Authority (FCA) proposed a number of changes to the asset management industry, adding it supported the disclosure of a single, all-in fee. It also said it would launch a market study into investment platforms.
"Rather than having the management fee and then also trading commission as well and then other sorts of fees on top of that, I think the regulator would rather that wealth managers charged just one fixed percentage that encompassed everything, so consumers would know exactly what they were paying," Rachel Winter, senior investment manager at Killik & Co, said.
Winter added that, because performance reporting has been a big part of Europe's upcoming Markets in Financial Instruments Directive, or MiFID II regulation, wealth managers had already been looking at their fee structures and considering one fee.
A weaker oil price was also a drag on UK blue chips, with shares in majors Royal Dutch Shell and BP both dropping nearly 1 percent.
Shares in mining firms Glencore and Antofagasta also fell following a dip in the copper price.
Shares in Bunzl, a provider of distribution and outsourcing services, bounced more than 4 percent and were the biggest gainers by some way on the FTSE 100.
Bunzl was set for its best day in a year after issuing an upbeat trading statement in which it said it saw a 7 percent rise in first-half revenue at constant currency, as well as a boost from recent acquisitions.
Outside of the large caps, results dragged down shares in Stagecoach, which slumped 8 percent after its full-year earnings missed expectations. Stagecoach's full-year pretax profit dropped 15.3 percent as economic conditions hit its domestic bus business.
"With no improvement in the outlook and further attention on the underperforming East Coast Rail franchise we would expect the shares to be weak today," analysts at UBS said in a note. (Reporting by Kit Rees; Editing by Mark Potter)