The controversial Bill that would allow colleges to award foundation degrees independently of universities has had its third reading in the House of Lords and will now move to the House of Commons.
Last week, the House of Lords defeated proposals contained in the Further Education Bill that would have given the Learning and Skills Council power to sack failing principals.
Universities UK said it still had concerns that extending foundation degree-awarding powers to colleges could have "serious unintended consequences" for collaborative partnerships between further and higher education.
However, it said, there had been "substantial" progress on its concerns, in particular on protecting progression opportunities for foundation degree graduates who wanted to move on to honours-level study.