* Graphic: sterling and gilt yields http://bit.ly/2dgAXn1
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv
LONDON, May 16 (Reuters) - Sterling inched back towards the top of its recent range against a broadly weaker dollar, though it again looked short of the power to push past $1.30 ahead of inflation numbers due at 0830 GMT.
The Bank of England weakened the pound last week by cutting its forecasts for the UK economy and pushing out its assumption for when it will raise rates to the end of 2019 - assuming Britain's exit from the European Union goes smoothly.
That involves it looking through a rise in inflation past its 2 percent target that has raised concerns over its likely impact on the consumer spending power that has kept UK growth going through a year of political turmoil.
Analysts said the forecast jump in inflation to 2.6 percent would still be in line with the Bank's own expectations and may not be enough to drive sterling past through resistance below $1.30 that has held for a month.
"There were a few hawkish takeaways from the inflation report last week but the market wasnt convinced about the legitimacy of the Banks assumptions of a smooth Brexit and an increase in wage inflation and failed to respond," said Rabobank strategist Piotr Matys.
After a late dip in the previous session, sterling was up a quarter of a percent at $1.2929 and 85.28 pence per euro in morning trade in London.
The biggest news so far this week has been a shift in futures market positioning data, showing bets against the pound were cut by the third most ever last week and are now less than half of a series of record highs hit over the past seven months.
That - stemming from a bounce for the pound after the announcement of a surprise election last month - would seem to mark a sea-change in investors' approach to the currency.
Yet it has struggled to make further progress and many major banks remain unconvinced the market can ride out 18 months of potentially bruising Brexit negotiations unscathed.
"Will the CPI data, followed by unemployment and wages tomorrow, then Easter-boosted retail sales on Thursday, prompt fears of increased MPC hawkishness? It's just about possible," said Societe Generale analyst Kit Juckes.
"But the pound has clearly risen against the dollar much more than would appear justified by yield differentials ... Still, the next three days are likely to see the last of the sterling short-covering rally." (Editing by Andrew Heavens)