John Gordon-Sinclair played the Captain's nephew, known as 'PK'. He took over as lighthouse keeper after MacKay's death (explained in the show as the Captain having 'returned to his first love, the sea'). PK made his debut on January 10th 1988 in 'Born To Wander', the first show of the fourth UK series.
As far as I've been able to work out, he stayed for two series, and his last appearance was most probably aired on December 11th 1988 (although I can't confirm that yet). From January 1989 the lighthouse was occupied by a new character, 'BJ', played by Simon O'Brien. I don't have any further information on him, although I'm reasonably certain he stayed to the end of the show's run, probably in mid-1990.
So far as I know, MacKay clocked up 48 shows ('Beginnings' - 'The Bells of Fraggle Rock', with the exception of 'Manny's Land Of Carpets'); Gordon-Sinclair did either 23 or 24 ('Red-Handed And Invisible Thief' - Sidebottom Blues' with the possible exception of 'Sprocket's Big Adventure') and O'Brien did the remainder, including 'Manny's Land Of Carpets'.
I do not yet have a full set of broadcast dates, hence the above may not be completely accurate, and it should be noted that the shows did not air in the same order in the UK as they did in the US.
I've also just discovered that the animated series was running concurrently with the live-action series in the UK, possibly starting in January 1990.