The pardon was arranged by Gerard Richardson, a wine merchant in Whitehaven and founder / CEO of the International Maritime Festivals. Richardson himself has explained that:
The John Paul Jones story was the foundation stone of the Maritime
Festivals and, during the first one in 1999, Jones was pardoned and
the US Navy was given the rare honour of the Freedom of Whitehaven
This part of the broader West Cumbria Tourism Initiative (WCTI)and
the Renaissance of Whitehaven project, the aims of which were to
develop tourism resources in a town that previously relied upon
traditional industries for its economic base.
Thus, sempaiscuba's comment is not far off the mark. The article Whitehaven Maritime Festival 1999 has more details:
On June 26th and 27th 1999 Whitehaven held its first maritime festival
celebrating the history of this once important port and looking
forward to a future as a marina and tourist location, thanks to a
massive investment in the harbour. The event was a huge success with
up to 100,000 people attending over the weekend. The weather was good
except on Saturday night when torrential rain poured down on a
re-enactment of John Paul Jones' raid of 1778.
According to the then harbourmaster Captain David Allan,
We offered them the freedom of the harbour, much like the freedom of
the town – you can send one of your military ships to Whitehaven once
a year and we won’t charge you any fees.
The Americans took this very seriously and that proclamation ended up
on the desk of Bill Clinton.
It’s now on display in the American navy academy at Anapolis [sic]
In short, Whitehaven has a maritime history and celebrating it has boosted the town's tourism. John Paul Jones, one of the best known historical figures associated with Whitehaven, is a part of that history and using this generated extra news coverage as the ceremony was conducted
in the presence of Lt. Steve Lyons representing the US Naval Attaché
to the UK, and Yuri Fokine the Russian Ambassador to the UK.
European Stars and Stripes (July 13, 1999), quotes Lyons:
The pardon represents the respect Jones has claimed over the years,
and certainly strengthens the bond between our nations and navies...
Jones also served in the Russian navy of Catherine the Great, hence the presence of their ambassador.