Defensive sectors such as telecoms and pharmaceuticals led gainers, as investors were unwilling to place bets on more risky sectors while a deal was yet to be finalised.
Banks fell by as much as 1.2 percent in morning trade, led by those with significant exposure to the euro zone, such as Royal Bank of Scotland and Lloyds.
However, they staged a partial recovery to trade down just 0.2 percent after news that Cyprus had agreed to spin off Greek units of its banks to Greece.
They weakened again as it became clear that a final deal would not be struck during trading hours. However, traders were reluctant to spark a sell-off, wary of the potential for a substantially higher open - or "bullish gap" - on Monday, should the crisis be resolved over the weekend.
"After last weekend's rather cackhanded bailout plan, we gapped lower, and the fear is that if we come to a new bailout agreement, we'll gap higher. So no one really wants to be caught short," Michael Hewson, senior market analyst at CMC Markets, said.
"But while a resolution may well assuage fears of a massive sell-off, overall Europe's underlying problems are still there."
The FTSE 100 index closed up 4.21 points, or 0.1 percent at 6,392.76 points, although the turmoil in Cyprus saw the index snap a 5-week winning streak despite the session's gain.
The FTSE 100 was down 1.5 percent on the week - its biggest weekly loss since November.
BP rose 1.8 percent after announcing an $8 billion share buy-back programme to reward investors after it sold its stake in its Russian unit TNK-BP. The 6.2 points it added to the FTSE 100 was enough to bring the index into positive territory.
"The buyback of $8 billion of shares in BP has seen them up since the open, and when they're up, with the banks holding up too, that tends to hold the FTSE itself up as well," said Mark Foulds, trader at ETX Capital.
BP aside, the most popular stocks were in more "defensive" sectors. Pharmaceutical AstraZeneca advanced 3.3 percent as new CEO Pascal Soriot received favourable reviews from analysts after a marathon eight-hour strategy update.
Telecom BT led the index with a 3.9 percent gain after a target price hike from Nomura. The two stocks combined to add over 8 points to the FTSE 100.
Topping the fallers was Burberry, which fell 4.1 percent after peer Mulberry issued a profit warning, fuelling fears of a drop in spending among affluent tourists.