London's top-flight index peaked at 6898.7 - just 50 points shy of its all-time record - before closing 44.4 points higher at 6873.6.
The strong session came after Ukraine president Petro Poroshenko said a "ceasefire process" had been agreed, while Russian president Vladimir Putin hoped a peace deal could be reached by Friday.
The advance was earlier driven by a report showing accelerating growth in the services sector in China, which added to optimism after a US manufacturing index reached a three-year high.
This was matched in the UK after it emerged the services sector grew at its fastest pace in 10 months during August.
But despite this service sector surge the Bank of England is expected to keep interest rates at 0.5 per cent today, which led to the pound slipping slightly against the dollar, at 1.65.
Sterling fell sharply on Tuesday on signs of a pick-up in support for a yes vote in the forthcoming referendum on Scottish independence.
Expectations that the ECB will announce further measures to prevent the moribund eurozone from slumping into depression failed to stop the pound slipping against the euro, at 1.25.
In stocks, the improved geopolitical situation boosted travel stocks as International Airlines Group rose one per cent or 5.3p to 370p and easyJet cheered 19p to 1364p.
Equipment rental company Ashtead led the FTSE 100 risers' board after posting well-received first quarter results.
The group reported record pre-tax profits, up 33 per cent to £120 million for the period ended July 31, as chief executive Geoff Drabble said it continued to capitalise on recovering markets. Shares rose more than three per cent, or 35.5p, to 1022p.
Spirit Pub Company was also ahead, climbing 1p to 78p, after it said full-year results for the 53 weeks to August 23 were expected to be ahead of market expectations - with analysts on average having pencilled in earnings of £57.3 million.
Hargreaves Lansdown led the FTSE 100 fallers board dipping almost six per cent after reporting pre-tax profits up seven per cent to £209.8 million for the year to June 30, a slowdown on the previous year's 28 per cent increase.
Its shares fell 66p to 1073p as it reported a 50 per cent fall in annuity business following the Chancellor's pension reforms.
The biggest risers on the FTSE 100 Index were Ashtead up 35.5p at 1022p, CRH up 48p at 1446p, Barclays up 5.8p at 228.1p and Experian up 22p at 1075p.
The biggest fallers on the FTSE 100 Index were Hargreaves Lansdown down 66p at 1073p, Admiral down 61p at 1264p, Fresnillo down 20.5p at 932p and BHP Billiton down 29p at 1891p.