* Pound drops towards $1.30 after GDP data disappoints
* Traders nervy before next week's Conservative party conference
* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Adds quote, updates prices)
LONDON, Sept 28 (Reuters) - Sterling fell half a percent on Friday after data showed that British companies had cut their investment in the second quarter of 2018 and the economy grew slightly slower than previously thought.
The pound had already been under pressure as investors' optimism for a Brexit trade deal has declined ahead of the ruling Conservative party's annual conference next week, while a late rally in the dollar further hurt the British currency.
Beginning the day at $1.3089, sterling dropped to as low as $1.3000, its weakest since Sept. 12, before recovering slightly.
The pound held up better against a broadly weaker euro and was down just 0.1 percent at 89.115 pence.
British companies cut their investment in the second quarter of 2018, with Britain's exit from the EU less than a year away, and the country's balance of payments shortfall grew more than expected, data showed.
The Office for National Statistics confirmed a previous estimate that Britain's overall economy grew by a quarterly 0.4 percent in the April-June period but lowered the annual growth rate in the second quarter to 1.2 percent from a previous estimate of 1.3 percent.
A Reuters poll of economists had forecast year-on-year growth of 1.3 percent and quarter-on-quarter growth of 0.4 percent.
Previous batches of data such as retail sales had pointed to an economy that performed relatively well in the third-quarter, helped by unusually warm weather and British consumers spending more.
May warned last Friday that Brexit negotiations with Brussels had come to an impasse, inflicting on the pound its biggest one-day loss since 2016.
The focus has now shifted to the domestic front for next week's annual Conservative party conference, where May will seek to overcome divisions within her party over her strategy for future relations with the EU when Britain leaves in March.
"We expect the pound to decline to $1.24 in three months and $1.20 in six months as Brexit approaches but a deal remains elusive," said Stephen Gallo, European Head of FX strategy at BMO Financial Group.
"We expect an eventual 'soft Brexit' agreement... but we think the odds of a 'cliff edge Brexit' will increase measurably before a withdrawal agreement takes shape," he said.
Gallo expects the pound to rebound to $1.29 in nine months and $1.41 in 12 months.
October also heralds the next EU summit, at which May is desperate to make headway towards a Brexit deal.
"The pound will remain ultra-sensitive to any Brexit-related news in October, with the main risk event falling mid-month on the 18th and 19th when EU leaders meet in Brussels to try to reach a divorce deal agreement," said Western Union Business Solutions' senior currency strategist Nawaz Ali. (Reporting by Tommy Reggiori Wilkes and Tom Finn Editing by Peter Graff)