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London shares cling to gains on trade optimism despite mixed signals

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* FTSE 100 up 0.2%, FTSE 250 rises 0.3%

* Hargreaves Lansdown up after Q3 update

* Burberry bounces on LVMH results

Oct 10 (Reuters) - London's FTSE 100 inched up on Thursday, as investors hoped for a U.S.-China trade deal despite mixed media reports on where the two countries stand, while investment platform Hargreaves Lansdown led gains after a strong trading update.

The FTSE 100 index was up 0.2% by 0707 GMT. The FTSE 250 added 0.3%, though a 6.2% slide in Homewares retailer Dunelm after third-quarter results limited gains.

A report that the U.S. was mulling a currency agreement with China as part of a partial deal that could see a planned tariff hike next week being cancelled offered some respite to markets, though a separate report said there was lack of progress in deputy-level talks held this week.

Among bluechips, Hargreaves Lansdown climbed 2.4% after reporting a rise in total assets and luxury brand Burberry added nearly 2% following French rival LVMH's robust quarterly results despite the Hong Kong protests. (Reporting by Muvija M and Shashwat Awasthi in Bengaluru; Editing by Bernard Orr)