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* FTSE 100 down 0.2%, FTSE 250 off 0.2%

Aug 16 (Reuters) - The FTSE 100 index continued its sell-off on Wednesday after data showed that underlying inflation remained high, building a case for more interest rate hikes by the Bank of England (BoE), while Marshalls fell on lower half-year profit.

The exporter-heavy FTSE 100 index fell 0.2% by 0704 GMT, languishing at over one-month lows as the sterling rose 0.14% to $1.2718, right after the data.

Annual consumer price inflation cooled to 6.8% in July from June's 7.9%, as the BoE and a Reuters poll of economists had predicted.

However, core inflation came in at a hotter-than-expected 6.9% in July, while service rose to 7.4% from 7.2% in June.

Industrial metal miners shed 1.1%, leading sectoral losses, after data showed top metals consumer China's new home prices fell for the first time this year in July, adding to a string of downbeat data from Beijing.

Mid-cap stocks also declined 0.2%.

Marshalls shares fell 1.1%, after the firm reported a 26% slump in half-year profit. (Reporting by Siddarth S in Bengaluru; Editing by Nivedita Bhattacharjee)