Shadow ministerial career
In his first year in parliament, Morgan worked on standing committees for the Finance Bill, the Housing Bill and the Steel Privatisation Bill. Labour leader Neil Kinnock rewarded Morgan for this work by appointing him to Labour's shadow energy team on 10 November 1988. He became a junior shadow minister for energy, where he was given responsibility for Labour's response to the government's electricity privatisation policy. When taking the role, Morgan said he intended to scrutinise the government's plans for electricity privatisation as he found "no virtues in converting a public monopoly into a private sector monopoly" and wanted to find "a better deal for consumers". During Morgan's tenure, the shadow energy team opposed electricity privatisation. He spoke beyond his brief, asking why Wales received less investment than Cornwall and Devon and exploring a now disproven conspiracy theory that the Spandau prisoner believed to be Nazi German deputy Führer Rudolf Hess was an imposter.
In the shadow energy team, Morgan initially worked under Tony Blair, the shadow secretary of state for energy from 1988 to 1989. He then worked under Frank Dobson, the shadow energy secretary from 1989 to 1992. According to The Independent, Morgan and Blair worked "harmoniously" together. In contrast, the New Statesman said Morgan "antagonised [Blair] at every step". Morgan himself believed that he was "highly regarded" by Blair. He supported Blair's attempt to get elected to the National Executive Committee of the Labour Party in 1992 and voted for Blair during his campaign for the Labour leadership in 1994, which he won.
On 30 July 1992, the recently elected Labour leader John Smith appointed Morgan as a shadow minister for Welsh affairs. He remained in this post after Tony Blair became Labour leader in 1994. At first, Morgan worked under Ann Clwyd, the shadow secretary of state for Wales from July 1992 to November 1992. He then worked under Ron Davies, the shadow welsh secretary from November 1992, serving as his deputy. He was also given responsibility for Labour's health policy in Wales.
In the Welsh affairs brief, Morgan targeted quangos in Wales for their alleged cronyism, unaccountability and lack of democracy. These quangos were unelected, publicly funded organisations whose leaders were appointed by the Conservative government. Under John Redwood's tenure as Welsh secretary, the Welsh Office was criticised for presiding over a large increase over the amount of quangos in the country, with people sympathetic to the Conservative Party often appointed to lead them. In 1979, there were 44 quangos in Wales. By 1994, there were 111. Quangos came to dominate Wales. In 1994, Morgan claimed that government plans would result in there being more people sitting on quangos than local councillors in the country. He refused to vote for the Welsh Language Act 1993; the act's main purpose was to set up a new quango called the Welsh Language Board. Morgan said Labour would abstain on the act "because we hope to have the opportunity before long to do the job properly. That will be done when we revisit the question of a Welsh language measure when we are in Government." When William Hague was Welsh secretary, Morgan staged a protest with other Welsh Labour MPs outside the 1996 Conservative Party Conference, where he claimed that the total cost of the quangos in Wales had reached £51.5 million.
To tackle the cost of the Welsh quangos, Morgan stated in 1996 that a devolved Welsh Assembly established by a Labour government would combine four quangos, the Welsh Development Agency, the Cardiff Bay Development Corporation, the Development Board for Rural Wales and the Land Authority for Wales to create an "economic powerhouse". The idea of establishing a devolved Welsh Assembly had been supported by Morgan, who was one of its leading proponents. He was involved in talks with the upper ranks of the Labour Party on devolution, becoming an important figure in drawing up its devolution policy for Wales. In the Welsh affairs brief, he campaigned for Welsh devolution, helping move the proposal for a Welsh Assembly further up the Labour Party's policy platform. He was a member of the Campaign for the Welsh Assembly and supported Wales Labour Action, a pressure group within the Labour Party that called for the establishment of a Welsh Assembly.
Morgan's opposition to the Welsh quangos, as well as his attempts to stop the construction of the Cardiff Bay Barrage, alienated the traditionalists within the Labour Party in Wales. These actions also made him a known troublemaker towards the Welsh political establishment. In Cardiff, Morgan faced hostility from the local political establishment in the Labour Party. He ultimately found the 1992–1997 parliament more challenging than the previous parliament. He had a difficult relationship with some of Tony Blair's inner circle, including his close confidant Alun Michael and his closest adviser Peter Mandelson.