LONDON - Sterling strengthened on Thursday after Prime Minister Theresa May survived a no-confidence vote from her party, but investors said the gains would quickly evaporate if Britain's parliament remains deadlocked over Brexit.

A weakened May was set to ask European leaders for help after a mutiny by more than a third of her lawmakers failed to dislodge her but showed the scale of opposition to her deal for exiting the EU.

The pound climbed after its best day in six weeks moved it off 20-month lows. But traders said that only reflected relief in the market -- likely to be fleeting -- that May had survived and that Britain still had a chance to leave the European Union in March with a deal.

With May now safe from a challenge from her own party, the currency's strength hinges on her ability to win concessions from the EU over her Brexit deal.

"With every `flesh wound' May seems able to bounce back, but last night's vote has brought home just how tough a task she faces," said CMC Markets' analyst Michael Hewson.

"It is highly unlikely the (Brexit) agreement will make it through parliament whatever tweaks May can wrangle out of EU leaders, so expect further sterling weakness," he added.

Investors have shied away from betting on the pound in recent months because of political instability and high volatility.

Sterling gained 0.3 percent to $1.2660 by 1050 GMT after rallying 1.1 percent on Wednesday. It rose 0.2 percent to 89.73 pence per euro.

Sterling is still near the bottom of its recent range and is headed for a weekly loss, with just over three months to go until Brexit and no further clarity on the outcome.

With Britain due to leave the EU, parliament's opposition has suddenly opened up possibilities. Among them are a disorderly exit with no deal or even another referendum on EU membership.

Most investors still think the British parliament will eventually back a "softer Brexit" rather than a clean break from the EU, although nervousness about the outcome has left the pound trading within tight ranges.

May is heading to a summit in Brussels after her meetings, with EU leaders so far this week have failed to yield the legal assurances on the Irish border that lawmakers are seeking.

(Reporting by Tom Finn; editing by Larry King) ((tom.finn@tr.com; +44 2075427508 ; Reuters Messaging: tom.finn.reuters.com@reuters.net))