* Brexit deal agreement initially boosts pound
* Deal still needs parliamentary approval, doubts linger
* Domestic stocks come off highs, UK yields fall (Adds details)
LONDON, Oct 17 (Reuters) - The surge in sterling and the rally in Britain's domestically-exposed stocks fizzled on Thursday as investors braced for a showdown in the UK parliament over the new Brexit deal agreed between Brussels and London.
European Commission President Jean-Claude Juncker said Britain and the European Union had, after a week of intense talks, sealed a new Brexit agreement.
Both sides had found a "legally operative solution" to avoid a hard border in Ireland - a key sticking point, EU chief negotiator Michel Barnier told reporters.
That sent the pound up as much as 1.1% to a five-month high and within a whisker of $1.30, while UK stocks that make most of their money at home surged.
But the gains were temporary as the Northern Irish Democratic Unionist Party (DUP) that British Prime Minister Boris Johnson relies on in parliament said it would vote against the deal at an extraordinary session on Saturday.
That revived fears that Johnson will suffer the same fate as his predecessor: a failure to get British lawmakers to support the plan for the departure, plunging the country into another round of uncertainty.
"Amid the optimism about a deal, it is important to remember that the agreement still has to be agreed by the EU27 heads of state as well as the UK parliament. As things stand, parliamentary ratification is far from certain," Dean Turner, an economist at UBS, said.
The pound was down 0.2% by 1235 GMT, hitting $1.2793 - far below the $1.2988 level touched earlier in the day.
Sterling has been on a rollercoaster ride recently, and is up 7% since early September when it hit the lowest since October 2016 at $1.19.
Volatility expectations for sterling over the next week have jumped to their highest since the 2016 Brexit referendum, underlying investors' nerves.
Against the euro, sterling dropped 0.7% to 87 pence, having earlier reached 85.77 pence.
The euro was buoyed by news of a deal and was last up 0.4% at $1.1116 while the dollar index fell 0.3%.
The UK's FTSE mid-cap stocks index was well off its day's high and was last trading up 0.3%. The blue-chip exporter-heavy FTSE 100 index rose 0.8% on sterling's reversal.
British government bond yields initially surged, with 10-year yields hitting 0.79%, their highest since July , before falling slightly on the day to 0.69%.
"It looks like we've got something that would be the basis for a vote," said Kit Juckes, macro strategist at Societe Generale. "Now we will try to scramble up if he (Johnson) has got enough votes to pass the deal through the parliament."
STOCKS AND RATE CUTS
The agreement on a deal, while still to face a parliamentary test, has triggered a rethink on the outlook for UK stocks.
JPMorgan's basket of London-listed companies that make their cash at home has enjoyed a meteoric rally in the past week.
In this period it has vastly outperformed the FTSE 100 and FTSE 250. The benchmark is considered a barometer of Brexit worries.
"While Parliament approval is still required, the news today should provide legs to the rotation from UK exporters to domestic plays," Barclays Capital European equities strategist Emmanuel Cau.
Optimism that a Brexit deal would be finalised saw money markets reduce expectations of rate cuts from the Bank of England. They now see a 60% chance of a quarter point cut next December versus 76% on Tuesday and 90% last week.