Ten-year gilt yields tumbled 7 basis points from Friday's close to a record low of 2.070 percent by mid-afternoon, according to Reuters data. Yields on the March 2014 gilt, the two-year benchmark, also hit a record low of 0.335 percent.

"Against that backdrop of summit disappointment, there's a new flight to quality in Bunds. Gilts are following with a slight lag," Citi fixed income strategist Jamie Searle said. "Today's very much a 'risk-off' day. Equities are quite a bit lower, and (euro zone) spreads are sharply wider, particularly Italy's," he added.

However, gilts pared some of their price gains after the relatively hefty supply on offer from the market at the Bank of England's weekly buyback of 3-10 year gilts. This attracted offers totalling 2.32 times the 1.7 billion pounds of gilts the BoE sought, up from 1.81 times a week earlier.

The March gilt future settled 62 ticks up on the day at 115.69, not far off a contract high of 116.00 hit earlier in the session, as share prices fell almost 2 percent on the day.

"We need to get used to seeing record lows in gilt yields in the coming weeks and months. In the next few weeks we could get down to 2 percent (for 10-year gilts), perhaps before the year-end at this rate," said Searle.

But gilts still underperformed German government debt. The future trailed its German peer by more than 30 ticks, and the yield spread between 10-year gilts and Bunds widened by 5 basis points on the day to 7 basis points.

All EU states barring Britain agreed to set stricter budget rules for the single currency area and to have euro zone states and others provide up to 200 billion euros in loans to the International Monetary Fund to help address the turmoil.

On Friday, BoE executive director Andrew Haldane told Reuters that markets responded much better to clear implementation plans than to less concrete policy commitments.

Investors are also making way for 7 billion pounds of gilt supply this week, although much of that will be offset by the Bank of England's quantitative easing purchases.

The DMO will sell 3 billion pounds of 10-year gilts on Wednesday and 4 billion pounds of five-year gilts on Thursday. The two bonds to be sold underperformed neighbouring securities on the curve, as investors positioned for the supply.

Lloyds Corporate Markets analyst Eric Wand said that thin volumes were exaggerating market moves, and that liquidity would continue to dwindle after this week's two gilt auctions by the Debt Management Office (DMO).

"Once we get the auctions out of the way, gilts will shut up shop," Wand said. "If you don't want to position in these markets you're going to liquidate pretty quickly. As depth and liquidity gets worse, moves get exaggerated. We're seeing this in currencies as well," he added.

On Tuesday, investors' main attention will focus on British inflation data, which at 5 percent still has a long way to fall if it is to meet the BoE's forecast of a level below 2 percent by the end of next year.