By Miriam Mukuru

Yields on U.K. government bonds, or gilts, edged lower as investor concerns eased following Andy Burnham's first speech since announcing his candidacy for prime minister.

Ten-year gilt yields fell to 4.729% following the speech, from 4.745% beforehand, Tradeweb data showed.

Burnham outlined a plan to drive growth in every part of the U.K., while vowing to reduce welfare spending in a "fair and lasting" manner. The announcement brought relief to investors worried about U.K.'s high public spending.

The potential new leader could face the same challenges as Prime Minister Keir Starmer, including frail economic growth and constrained public finances, Capital Economics said in a note. A leadership transition could take place in July if no candidate challenges Burnham for the role.

The latest public sector net borrowing data showed government borrowing stood at 23.3 billion pounds ($30.76 billion) in May, 30% higher than a year ago, and 5.6 billion pounds more than the forecast by the fiscal watchdog Office for Budget Responsibility.

High public debt and weak finances leave limited room for the government to increase spending, Guilhem Savry, head of strategy research at Edmond de Rothschild Group said in a note.

Burnham has vowed to uphold the current fiscal measures, which say that day-to-day government costs will be met through tax revenue, rather than borrowing, alongside a commitment to reduce debt as a share of national income by the end of this parliament's term in the fiscal year 2030.

However, analysts expect a possible jump in government borrowing and increased taxes to meet rising spending requirements, including higher defense spending. Concerns about U.K.'s fiscal and economic outlook are likely to keep yields on its government bonds relatively high compared with other advanced markets.

"We think the risks lie towards borrowing costs rising in the coming months, rather than falling sharply," Pantheon Macroeconomics economist Elliott Jordan-Doak said in a note.

Investors await the naming of a new Treasury chief to replace Rachel Reeves for further clues on the direction of Burnham's economic and fiscal policies. This decision is likely to be the main influence on the gilt and sterling market in the near term, strategists at Goldman Sachs Research said in a note.

Potential candidates for the role include Ed Miliband, Wes Streeting, Shabana Mahmood, and Yvette Cooper, according to media reports.

Streeting is seen as a more business-friendly contender, compared with the others, due to his opposition to policies involving higher taxation and spending, Matthew Ryan, head of market strategy at Ebury, said in a note.

"A left-leaning appointment--e.g. Ed Miliband--would likely be received less favorably," analysts at Daiwa Capital Markets Europe said in a note.

Write to Miriam Mukuru at miriam.mukuru@wsj.com