* Worries about UK-EU ties come as UK economy weakens
* Pound seen extending slide
* 'Brexit' risk could harm investment into UK
LONDON, Jan 23 (Reuters) - Prime Minister David Cameron may have sown enough uncertainty about Britain's membership of the European Union to potentially sour investor sentiment towards UK stocks, bonds and sterling.
In a much-anticipated speech, Cameron promised on Wednesday to hold a referendum on whether the country should stay in the EU if his government is re-elected in 2015.
While UK financial assets did not lose much ground during or after the speech, there are concerns that a prolonged debate on whether Britain should stay in the EU may have a damaging impact on business and investment, as Deputy Prime Minister Nick Clegg later commented.
That would be an additional worry for international investors, who are already concerned about Britain's sluggish economic activity and the risk that it will lose its prized triple-A credit rating.
"Cameron needs to explain clearly what his policy is to the international investors who put their faith and money in UK corporates," said Simon Derrick, head of currency research at Bank of New York Mellon.
"The real 'so what' is that on top of the issues with regard to the economy and the UK's credit rating we could also get political uncertainty."
Derrick said the euro therefore had the potential to push towards 90 pence against sterling, more than six percent above its current levels.
Given analysts do not expect any referendum to be held for several years, it means a long period of uncertainty for UK assets.
Against this backdrop, an important driver of investor sentiment towards UK assets will be how euro zone politicians and business leaders react to Cameron's demands for a new settlement with the EU.
So far, the signs are unpromising. (Click here for more stories on reaction .)
"Overall, it's a very confused speech. A lot will probably think 'What the hell is he thinking?'," said Marc Ostwald, fixed income strategist at Monument Securities.
The damage the EU membership debate could inflict on UK assets is all the greater given investors are growing less worried about the euro zone crisis, from which sterling and gilts had been a bolt-hole.
The premium that investors demand to hold UK government bonds rather than German ones would therefore widen from around 44 basis points currently. At the height of the euro zone crisis in late 2011, the yield on the UK 10-year bond fell below its German counterpart.
Barclays economist Simon Hayes said even though the chances of a UK exit from the EU were remote, uncertainty over the issue would "make it harder to attract inward investment".
This is expected to influence investors' appetite for UK stocks. Small- and medium-sized British firms, which tend to be more reliant on sales to the EU than FTSE 100 companies, would be the most exposed to the EU membership debate.
Any turn in this debate that suggested exporting goods or services to the EU might become harder or more costly for firms would hurt UK stocks more broadly.
However, Gerard Lane, an equity strategist at Shore Capital, said large British companies which earn most of their income from abroad, such as Unilever, BAE Systems and Rolls-Royce, would be most sheltered from any downdraft in UK stocks.