UPDATE 2-Brexit worries pressure London shares, Europe steady

(For a live blog on European stocks, type LIVE/ in an Eikon news window)

* FTSE 100 down 0.5%

* Supreme Court rules UK PM's parliament suspension unlawful

* European travel stocks extend gains on Thomas Cook collapse

* Healthcare, utilities rally (Adds fresh comments, updates to prices to close)

By Susan Mathew

Sept 24 (Reuters) - European shares closed little changed on Tuesday on persistent growth worries and as London stocks succumbed to heightened Brexit uncertainty after the Supreme Court ruled that the British prime minister's suspension of parliament was unlawful.

The pound rallied as the Court's decision was seen as reducing the probability of Britain leaving the European Union without a divorce deal or possibly delaying Brexit.

The currency's rally saw the FTSE 100 give up 0.5% as firms that earn much of their revenue in dollars fell. More domestically focused stocks also declined 0.6%, showing deeper Brexit malaise among investors.

Opposition leaders called on Prime Minister Boris Johnson to resign, but a source in his office said he would not do so and remained committed to delivering Brexit on Oct. 31.

"We put the chances of a (Brexit) deal at just 10%, a no deal at some point at 40%, more delays at 45% and remain (in the EU) at 5%," said Paul Dales, chief UK Economist at Capital Economics.

"What we do know is that the performance of the UK economy will remain below-par until it is resolved."

Euro zone stocks and the broader STOXX 600 index both closed steady, giving up meagre gains as disappointing U.S. consumer confidence was the latest in a raft of poor economic data. After dismal data from Germany and across the euro zone had dented sentiment on Monday, a slight rise in German business morale did little to calm investor nerves as the Ifo economic institute said Europe's largest economy is still likely slipping into recession.

"(The German data) does not take away the fact that the German industry continues to suffer from structural changes and the ongoing trade conflict," said Carsten Brzesk, chief economist at ING Germany.

"While a "light" technical recession is not the end of the world for an economy... it is the lack of any signals of an imminent rebound which is more concerning."

Investors bought into sectors perceived as defensive plays such as healthcare, food and beverages and utilities - commonly considered as industries where demand and results hold up relatively better when economic growth slows.

Travel and leisure saw a 1.2% jump, the largest of any sector, as airlines and travel operators rose on expectations that they will pick up lost business from British travel giant Thomas Cook following its collapse on Monday.

TUI jumped 6.5% to top the main index, while Deutsche Lufthansa, Ryanair Holdings and EasyJet gained between 1% and 2%.

Belgian materials and technology group Umicore rallied 5.8% after it partnered with LG Chem for a cathode material supply deal.

Falling iron ore prices hurt miners such as BHP and Rio Tinto, while lower oil prices hit oil stocks .

The eurozone banking index and auto stocks continued their slide after Monday's business activity readings. (Reporting by Shreyashi Sanyal, Sruthi Shankar and Susan Mathew in Bengaluru; Editing by Gareth Jones)