Answer by taking a quote from the following article:

Chumbawamba  were a British band that formed in 1982 and dissolved in 2012. The band constantly shifted in musical style, drawing on genres such as punk rock, pop, folk, and experimental. Their anarchist or libertarian socialist political stance exhibited an irreverent attitude toward authority, and the band have been forthright in their stances on issues including animal rights, pacifism (early in their career) and later regarding class struggle, feminism, gay liberation, pop culture and anti-fascism. The band are best known for their song "Tubthumping", which was nominated for Best British Single at the 1998 Brit Awards.

By the mid-1980s Chumbawamba had begun to release material using the vinyl format on their own Agit-Prop record label, which had evolved from an earlier project, Sky and Trees Records. The first release was the Revolution EP in 1985, which quickly sold out of its initial run, and was re-pressed, reaching No. 4 in the UK Indie Chart, and staying in the chart for 34 weeks. The first LP, Pictures of Starving Children Sell Records (1986) was a critique of the Live Aid concert organised by Bob Geldof, which the band argued was primarily a cosmetic spectacle designed to draw attention away from the real political causes of world hunger.  The band toured Europe with Dutch band the Ex, and a collaboration between members of the two bands, under the name "Antidote", led to the release of an EP, Destroy Fascism!, inspired by hardcore punk band Heresy, with whom they had also toured. Both the Ex and Chumbawamba were released on cassette tape in Poland during this period, when music censorship was entrenched in Iron Curtain nations. The "RED" label, based in Wroclaw in south-west Poland during the late 1980s, only released cassette tapes and, despite the limits enforced by Polish authorities, was able to release Chumbawamba's music, in addition to bands from the USSR, East Germany and Czechoslovakia.  Chumbawamba's second album, Never Mind the Ballots...Here's the Rest of Your Lives, was released in 1987, coinciding with the general election, and questions the validity of the British democratic system of the time. The band adopted another moniker, Scab Aid, for the "Let It Be" song release that parodied a version of the Beatles song recorded by the popstar supergroup Ferry Aid to raise money for victims of the Zeebrugge ferry disaster.  The 1988 album English Rebel Songs 1381-1984, originally released as English Rebel Songs 1381-1914, was a recording of traditional songs.

Did they have any other hits during that time?