By Alun John

LONDON (Reuters) - Sterling was at its strongest against the euro in two-and-a-half years on Wednesday, supported by a relatively hawkish Bank of England and political uncertainty in France and Germany, though it dipped against a strengthening dollar.

The euro dropped as low as 82.35 pence, its lowest since March 2022, though was last a fraction stronger on the day at 82.50 pence.

More notably, a break past March 2022's 82.035 pence would take the euro to its lowest on the pound since June 24 2016, the day of the outcome of Britain's vote to leave the European Union.

"A little question seems to have popped up over the last few weeks, perhaps amongst the mainstream press, asking whether or not euro sterling could finally go back down to where it was before the referendum in 2016," said Jane Foley, head of FX strategy at Rabobank.

"That would be on the back of this perception that the ECB is more growth-oriented - or lack of growth-oriented - and we've got these political issues, clearly in France and in Germany."

"We can sit here and quite easily list out what is wrong with the UK economy and what is wrong with the UK budget ... but at least there is a budget. And given the consensus view that the Bank of England will need to be perhaps more cautious than the ECB, sterling is finding a little bit of support," she said.

The Bank of England is expected to leave rates steady next week and be cautious next year. Markets are pricing just three 25 bp rate cuts by the end of next year.

In contrast, the European Central Bank meets Thursday and is expected to cut rates by 25 basis points, and analysts expect the ECB to cut at every meeting at least for the first half of 2025, and possibly beyond.

Weak economic growth at the heart of the euro zone is contributing the ECB's dovishness, and there is also politics in the mix.

The collapse of Prime Minister Michel Barnier's government last week left France's 2025 budget in limbo with ministers scrambling to prepare stop gap legislation to roll over 2024 spending limits until a new budget bill can be drafted next year.

Germany's governing coalition collapsed last month.

It was a different picture for the pound against the dollar, last down 0.34% at $1.2728.

The dollar strengthened across the board on Wednesday, as traders feared U.S. inflation data due later in the day could come in hotter than expected and disrupt bets on a Fed rate cut this month.

(Reporting by Alun John; Editing by Andrew Cawthorne)