The FTSE 100 rose 0.4 percent to six-month high. The FTSE 250 had eased 0.1 pct by 0817 GMT.
Shell rose 2 percent to a six-month high and BP also gained as oil prices rose on anticipation of tightened supply after the United States said it would end all Iran sanction exemptions by May.
Airline stocks suffered as oil prices rose, however. Easyjet fell 3.7 percent and British Airways-owner IAG shed 2.5 percent on the main index. Wizz Air lost 3.4 percent on the mid-cap index.
"Suddenly we're back to supply uncertainty being a graver threat than demand uncertainty," said Markets.com analyst Neil Wilson. "This risks a very real prospect of an abrupt spike in prices if there is not enough supply to fill the gap. Risks seem skewed to the upside for oil and we may see a pop higher still."
Precious metals mining company Fresnillo slipped 2.5 percent as gold prices fell after the dollar gained and BMO downgraded the stock on Monday.
Shares of BT Group fell 1 percent after Reuters reported that an investigation into an accounting fraud in the company's Italian unit had uncovered more evidence senior executives had inflated the division's financial performance.
Small-cap Thomas Cook rise nearly 18 percent, on course for its best day in more than four months, after Sky News reported the tour operator had been tentatively approached by several parties about taking over its tour operations or the entire company.
However, investors were cautious as they returned from the Easter holiday, amid speculation China may tone down its stimulus measures after last week's first-quarter economic data showed unexpected signs of recovery.
In the UK, talks between Prime Minister Theresa May and the opposition Labour Party over Brexit are set to resume, but media reported her fellow Tories are preparing new attempts to oust May.