Michael Gove today became the first member of the cabinet to urge people to vote tactically for the Liberal Democrats in the May local elections, as he fended off attacks on the abolition of the Educational Maintenance Allowance.

In an attempt to spike the guns of Labour and Lib Dem critics campaigning against the scrapping of the £30 weekly allowance, Gove praised Lib Dem councils that help students with travel costs.

The education secretary's comments came ahead of a defeat in the Commons tonight of a bid by Labour to keep the allowance; it was defeated by 317 votes to 258, a government majority of 59.

Gove's remarks highlight the support among senior allies of David Cameron for greater co-operation with the Tories' coalition partners. He hailed Lib Dem and Conservative councils that are helping students by upholding their statutory commitment to fund student travel.

"Essex raised travel costs for children in receipt of a range of benefits, and in Hull, Liberal Democrat-controlled Hull, any student in receipt of Education Maintenance Allowance also gets a travel grant to cope with the full cost," he told MPs.

"Well they won't if a Labour council takes power, I suspect. But if they're wise enough to vote Liberal Democrat at the next local elections in Hull …"

Amid gasps and laughter, Gove paused before adding, "… or for the Conservatives in any seat where we are well placed to defeat Labour, then they will have a council which is fulfilling its statutory duty. It is no surprise that there are Liberal Democrat and Conservative councils which are ensuring that all students receive the support they deserve. It's striking that this is in addition to Education Maintenance Allowance."

The intervention by Gove, a close friend of the Tory MP Nick Boles who last year urged an electoral pact between the Conservatives and Lib Dems, was designed to show how the coalition partners are working hard to soften the impact of the allowance at a local level.

Students march to Parliament Square ahead of the debate on whether the Education Maintenance Allowance should be scapped guardian.co.uk

The government announced that it would save £500m by targeting the allowance at needy students. Ministers believe that the current system, which pays as much as £30 a week to less well-off students aged 16 to 19, could be better targeted at poorer students.

Simon Hughes, deputy leader of the Lib Dems who is the government's adviser on access to education, used today's debate to voice concerns at scrapping the allowance.

He told the shadow education secretary, Andy Burnham: "There is concern across the house about the policy to get rid of EMAs without a sufficient replacement. Can I say to him, as I have said privately, I will work with him, as I am working with the secretary of state, to make sure, as far as I can, that the successor scheme achieves the objectives that are in his motion as in the government's amendment. If, together, we can do that then together we will improve the reputation of this house."

Burnham, who held talks with Hughes ahead of today's Labour-inspired debate, dismissed his remarks.

"I don't think what he has just said will be good enough for young people listening to this debate whose lives will be directly affected by the loss of EMAs. Promis[ing] to work with the secretary of state with an unspecified amount of money to deliver an unspecified result is really not going to do the job for them. Do they want to keep the benefits of this successful scheme, do they want to see the same numbers of young people in further education in their constituencies? Or are they prepared to take a risk on this secretary of state and this Tory-led government?"

Talks between Hughes and Burnham had collapsed before the debate. Hughes proposed an all-party group to examine the allowance's replacement. Labour had insisted the principle of a weekly national payment be maintained.

In the debate Gove reacted angrily when Burnham quoted an article by his wife, the Times journalist Sarah Vine, to show the Tories were out of touch.

She wrote last week: "Like all angst-ridden working mothers I live in terror of upsetting my cleaner." Burnham, MP for Leigh in Greater Manchester, said: "Now, I can tell you, angst-ridden mums in Leigh talk of little else. I do sympathise with Mrs Gove's predicament. But I wonder if the secretary of state might pass on a bit of advice to all the wives of cabinet colleagues who fret about the same curses of modern living.

"Can I respectfully suggest that the best way to stay on the right side of the cleaner might not be to clean the oven oneself, but instead to press one's other half not to remove the cleaner's kids' EMA."

• This article was amended on 20 January 2011. The original quoted Michael Gove as saying "Essex razed travel costs for children in receipt of a range of benefits". This has been corrected.