The June gilt futur settled 11 ticks higher on the day at 116.93, while the equivalent German Bund future rose by 17 ticks.
Strategists said markets were preparing for Tuesday's auction of 3.5 billion pounds ($5.66 billion) of the 3.75 percent September 2021 gilt.
It will be the UK Debt Management Office's first auction of the 2011/12 financial year, and the first gilt sale of any type since it last sold the same gilt on March 17. On Wednesday, a second auction will offer 1 billion pounds of 1.125 percent index-linked gilts due 2037 .
"We've got two lots of supply. It's a little bit of a test," said Marc Ostwald, strategist at Monument Securities. "The big question is what sort of concession we need to build in to get the supply away."
Tuesday's other main focus will be the release at 0828 GMT of the PMI index for Britain's dominant services sector, which is expected to be little-changed on the month, according to a Reuters poll of 27 economists.
March's construction PMI index, released earlier on Monday, showed activity held up much better than expected, with growth continuing at a rate close to February's 8-month peak.
Market reaction to that news was muted and analysts said investors were more concerned about Britain's above-target inflation and wider factors, such as the euro zone debt crisis.
"I don't think the services PMI's going to have a very profound impact," Ostwald added. "The more important aspects are actually the inflation numbers and what goes on elsewhere."
Although the services PMI index does not include the retail sector, economists are still worried that poor consumer morale since the start of the year will hit related service industries.
While this is positive for gilts in the short-term, by pushing back the likely date of the BoE's first rate rise in a new tightening cycle, longer term it may weaken the British government's ability to cut the budget deficit, said Lloyds strategist Eric Wand.
"A slow growth environment is normally good for fixed income," he said. "But the bigger risk is if that growth impacts the fiscal ambitions of the government.
"The market certainly hasn't taken that on board yet. Were more people to start to question that, there would be risk from that angle."
Ten-year gilt yields fell by one basis point to 3.72 percent, underperforming the two-year gilt by the equivalent of 1 basis point. Yields had touched three-week highs on Friday.
The 10-year gilt yield's spread versus Bunds was little changed from around 1530 GMT on Friday at just over 35 basis points, following several days of underperformance after the spread reached its tightest in 17 months last Tuesday.