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* Unilever hits over three-month high

* Airlines feel the heat as oil climbs

* Discount retailer B&M slides on profit warning

* FTSE 100 up down 0.1%, FTSE 250 off 0.6%

May 31 (Reuters) - London's FTSE 250 index fell on Tuesday and marked a second straight month of losses on concerns a worsening cost-of-living crisis would hurt economic growth, while shares of airlines fell as oil prices climbed.

The domestically focussed midcap index closed 0.6% lower. Airlines such as easyJet, Wizz Air and British Airways owner IAG slid between 3.3% and 5.6% as Brent crude climbed above $120 a barrel, signalling rising fuel costs.

The blue-chip FTSE 100 index ended 0.1% higher lifted by Unilever's shares which jumped 9.4% after the consumer goods giant named a billionaire activist to its board, heaping pressure on the company for a bigger revamp of strategy.

Gains on the index were capped by B&M whose shares tumbled 15.0% after the discount retailer warned of lower profit margins this year as customers spend less on discretionary products due to red-hot inflation.

"That's not the message the market wanted to hear from B&M, even if the company is in a considerably stronger place than it was pre-pandemic," said Russ Mould, investment director at AJ Bell.

"B&M's value-based proposition means margins are pretty skinny and therefore vulnerable to inflation."

The FTSE 100 ended May with a 0.8% rise, buoyed by sharp gains in oil and gas and banking stocks , while its domestic counterpart fell 1.4%, adding to year-to-date losses of over 13.1% as concerns about a recession in Britain mounted.

Credit card borrowing in Britain rose last month at the fastest annual rate since 2005, possibly reflecting a worsening cost-of-living squeeze that may now be starting to slow the housing market, Bank of England data suggested on Tuesday.

Among other stocks, Pennon Group fell 2.7% after it warned of a near-term impact to earnings amid the higher inflationary environment. (Reporting by Sruthi Shankar and Devik Jain in Bengaluru; Editing by Bernadette Baum)