He featured in the final of the Intercontinental Cup, won the Svenska Cupen in 1980, and helped the club to a second-place finish in the Allsvenskan.
In his three years at Ewood Park, Parkin made 13 league appearances, all but one of which were as a stand-in for the injured Glenn Keeley towards the end of the 1978–79 season.
He also featured in the 1980 Svenska Cupen final, which ended in a penalty shoot-out victory over IK Brage at the Råsunda Stadium.
Parkin left Malmö Stadion and returned to England in August 1981 with Bristol Rovers, though had to spend a day as an Almondsbury Greenway player to get around rules governing Swedish transfers.
He was voted Player of the Season after he scored four goals in 54 games in 1987–88, as Lou Macari's side secured a comfortable mid-table position.
[1] However, he lost his place in August 1991 and was loaned out to Shrewsbury Town the next month, featuring in five Third Division games for John Bond's "Shrews" at the Gay Meadow.
He returned to Vale Park the next month only to be handed a free transfer in May 1992, having played just eight games for the "Valiants" in the 1991–92 relegation campaign.
Parkin departed Feethams and moved on to Barrow of the Northern Premier League in November 1993, where he was made player-assistant manager, before retiring as a player following a broken leg.