* World FX rates in 2020 http://tmsnrt.rs/2egbfVh

* Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv

LONDON, Dec 28 (Reuters) - Sterling touched a fresh five-month high against a broadly softer dollar on Thursday, putting the currency on track to end the month with gains of more than 1.3%.

At 1019 GMT sterling was unchanged at $1.28, after earlier hitting $1.2825, its highest level since Aug. 1.

The dollar is dipping as traders increase bets that the U.S. Federal Reserve will slash interest rates in 2024 amid moderating inflation.

Inflation is also slowing in the UK, with data earlier in December showing a surprise drop in British CPI for November.

"The Bank of England is showing more wariness than the Fed about the trajectory for inflation, so any sign that interest rates might stay higher for longer, in the UK, aren't read well for the housing market," said Susannah Streeter, head of money and markets at Hargreaves Lansdown.

Data on Dec. 20 showed UK house prices fell in October by the most since 2011.

The figures came after the BoE held rates at its final policy meeting for 2023 on Dec 14. Market players are now betting on around 150 basis points of interest rate cuts by the BoE during 2024, though they place a 94% chance that there will be no change at the next meeting on Feb. 1.

Elsewhere, traders are looking ahead to 2024 after Wednesday's announcement that UK finance minister Jeremy Hunt will present the spring budget on March 6, in what is likely to be the government's last major chance to prepare the ground for an election that must be held by January 2025. (Reporting by Lucy Raitano; Editing by Kirsten Donovan)