* FTSE 100 down 0.8%, FTSE 250 down 1.1%
* No-deal Brexit concerns hit domestic shares
* LSE biggest blue-chip loser after HKEX cancels bid
* Recruiting firms slump after weak trading updates (Adds company news items, updates share moves)
By Muvija M and Shashwat Awasthi
Oct 8 (Reuters) - UK-focused stocks from Tesco to housebuilders sank on Tuesday as worries over a no-deal Brexit peaked after a Downing Street source said a divorce deal was essentially impossible, while LSE dropped after the Hong Kong bourse dropped its takeover bid.
The FTSE 250 index, whose constituents make half their earnings from the UK, stumbled to its lowest in more than a month and ended 1.1% lower.
The blue-chip index, also vulnerable to hits from a deterioration in the global trade scenario, dropped 0.8% ahead of the much-anticipated resumption of U.S.-China negotiations this week.
At home, Brexit took centre stage again amid fears that any potential agreement between Britain and the European Union was dead in the water as both parties positioned themselves to avoid blame for another extension or a chaotic no-deal Brexit.
Those fears translated into a sell-off in shares of companies perceived to be most exposed to a fallout from Brexit.
An index of retailers slipped 2.5% on its worst day in over four months, with Tesco falling 3%, and homebuilders losing 1.3%.
"We are now heading towards the Revoke versus No Deal showdown," Markets.com analyst Neil Wilson said.
Aside from Brexit, the Sino-U.S. trade talks, scheduled for Oct. 9 and 10, could also make or break stock market performance this week.
However, mixed signals from Washington, which expanded its trade blacklist of Chinese companies, have done little to settle investor nerves in the run up to the meetings.
Market participants are still licking their wounds after a sell-off in global markets that had pushed the FTSE 100 to its worst week in a year as growth worries and recession risks peaked.
Ahead of the talks, corporate news also drove some market moves.
LSE fell 5.8% after Hong Kong Exchanges and Clearing scrapped its unsolicited $39 billion offer, leading shares of the UK bourse operator to levels not seen since last month when HKEX first announced the takeover plans.
The stock also suffered its steepest one-day decline since the 2016 Brexit referendum.
Recruiters PageGroup and Robert Walters dropped 12% and 6%, respectively, after they revealed that a host of macroeconomic troubles including the U.S.-China trade war, Hong Kong protests and Brexit is hindering performance.
Rivals Hays, SThree and Staffline skidded between 2.6%-7.3% as a result.
EasyJet was the biggest drag on the index with a 7.5% slide, despite a robust outlook for the current year as the carrier said it expected capacity growth in 2020 at the lower end of its historic range.
British Airways owner IAG also lost nearly 2%, while smaller player Ryanair gave up 1.5%.
(Reporting by Muvija M and Shashwat Awasthi in Bengaluru, additional reporting by Tanishaa Nadkar; Editing by Bernard Orr and Alexandra Hudson)