UK housing market may be starting to moderate -RICS

* House price growth starting to ease - RICS

* London price balance hits lowest since March 2013

* CML data shows mortgage lending continues to rise (Adds Council of Mortgage Lenders data)

LONDON, July 10 (Reuters) - More signs emerged last month that the upturn of Britain's housing market is starting to moderate, even in hotspots like London, although mortgage lending continues to rise, surveys showed on Thursday.

The Royal Institution of Chartered Surveyors' monthly house- price balance eased to 53 in June from a downwardly revised 56 in May, slightly below the forecasts in a Reuters poll of economists.

Chartered surveyors said tighter mortgage lending standards introduced in April were slowing the volume of transactions, along with "heightened rhetoric" from the Bank of England about the possibility of higher borrowing costs.

A separate report from the Council of Mortgage Lenders (CML) suggested the new mortgage standards had a subtle rather than dramatic effect on mortgage lending during May.

"The BoE's recent introduction of a ceiling on high loan-to-income lending and a 3 percent interest rate stress test is unlikely on its own to have an immediate influence on the market," said Simon Rubinsohn, RICS's chief economist.

"However, rhetoric from key officials at the Bank, including Mark Carney, alongside the consequences of the introduction of (tighter mortgage standards) are already slowing momentum, particularly in London."

The CML data showed the both the number and value of loans to home movers rose 8 percent in May from April. Compared with a year ago, the number of loans rose by 9 percent, and they were 21 percent higher in value.

"First (Other OTC: FSTC - news) -time buyers and home movers continue to be key drivers in market growth and their activity does not seem to have been noticeably disrupted (by stricter mortgage standards)," said Paul Smeel, the CML's director general.

A survey by mortgage lender Nationwide showed last week that London house prices soared 26 percent over the past year, the biggest annual jump since 1987.

But the RICS report suggested that growth is unlikely to be sustained at that level in the capital. Its London price balance fell to the lowest reading since March 2013 last month and is now below the national average.

Another survey, from mortgage lender Halifax on Wednesday, also suggested the housing market is cooling a touch. It showed prices unexpectedly slipping last month but rising 8.8 percent compared with June last year. (Reporting by Andy Bruce; Editing by William Schomberg and Larry King)