LONDON, Aug 13 (Reuters) - The pound rose on Tuesday after data showed Britain's unemployment rate unexpectedly fell in June, although wage growth slowed.

Figures showed the UK jobless rate dropped to 4.2% in June, down from 4.4% in May and below expectations of a rise to 4.5%.

Sterling was last up 0.24% at $1.2797, from $1.2779 before the data. The euro was down 0.15% against the pound at 85.49 pence.

Separate figures showed average weekly earnings excluding bonuses were 5.4% higher than a year earlier in the three months through June, down from 5.8% in May. (Reporting by Harry Robertson, editing by Alun John)