John Nettles actually drove two different Triumph Roadsters in the series (which ran from 1981 to 1991): a 1800cc model from 1947 and a 2000cc from 1949. Wikipedia notes that there were colour differences, but "in some episodes both cars appeared purporting to be the same car."
1610 J seems to have been the genuine registration number of the first car – this being in the standard format for cars registered in Jersey. The second car was sold to the BBC in 1985 by its original owner, a Mr. Brook Fowler. The BBC changed the registration number of this car from the original KLX 322 to 1610 J.
This second car fetched £37,000 when it was auctioned, following the end of filming, in aid of Children in Need. Since then it has been used to raise more funds for charity – it's been driven from Land's End to John O'Groats on two occasions, most recently in 2000 in order to raise funds for the Cornwall Air Ambulance.
Between 1991 and 2013 the car had at least two different owners (neither of whom appears to be famous in any way). It was auctioned again in 2013, fetching £27,000. The latest news of it seems to be that it attended the Celebrity Antiques Roadshow Trip in June 2014; this comes from a page on ClassicCarsForSale.co.uk, which claims to have the car for sale but has no obvious date and no obvious link to an actual listing.
Other details are on the website of Bonhams, the auctioneers that sold the car in 2013.
© Haydn Thompson 2021