Markets paid a lot of attention to the US Fed's dot projections (somewhat ironic, given the FOMC's reported views about the wisdom of publishing those projections). The Fed's statement, however, increased the focus on inflation.
Inflation pressures do seem to be building in an inexorable fashion in the US. Core inflation was again above expectations. "Data dependency" does not mean "focus on a single data point" – but the trend of core inflation has been rising, and is suggestive of cost push pressures.
Inflation is a local issue – the correlation of core inflation rates across the OECD is basically zero – so the return of US inflation pressures does not tell us anything directly about the Euro area final CPI data today. The market is not looking for a change from the flash estimate.
The Bank of England is not likely to offer any interest to markets, given political events are the focus for investors in the UK. The US Philly Fed business sentiment survey may raise a flicker of interest however.