SYDNEY (Reuters) - Australian consumer sentiment fell in July as fears about a possible rise in borrowing costs overshadowed the prospect of lower taxes and government relief on power bills, a survey showed on Tuesday.

The Westpac-Melbourne Institute index of consumer sentiment slipped 1.1% in July from June, when it rose 1.7%. The index reading of 82.7 showed pessimists far outnumbered optimists.

"Sentiment remains stuck in the same deeply pessimistic range that has dominated for two years now," said Westpac senior economist Matthew Hassan.

"Fears of persistent inflation and further interest rate rises are again weighing more heavily on the consumer mood, offsetting any boost from the arrival of the tax cuts and other fiscal support measures."

Most workers will receive a cut in income taxes from this month, though the money has likely not shown up in pay packets yet.

The Reserve Bank of Australia (RBA) held rates steady at its last policy meeting in June but warned of upside risks to inflation that could require further tightening.

The survey found the proportion of respondents expecting higher mortgage rates in the next 12 months climbed to almost 60% from 48.3% in June.

As a result the survey's measures of family finances both dropped sharply, overwhelming a small improvement in the economic outlook.

The index measuring whether it was a good time to buy major household items did bounce 3.1%, but remains historically low at 82.1.

(Reporting by Wayne Cole; Editing by Jamie Freed)