Mr Horn, a former Communist who as foreign minister in 1989 played a key role in the decision to open the border with Austria and thereby knock down the Iron Curtain, is likely to express concern over the apparent slowness with which Hungary and its Central European partners are being welcomed into the Western fold.
He will also be trying to encourage British entrepreneurs to show more interest in his country, the first of the former Warsaw Pact bloc to open its doors to the free market.
"We would certainly welcome more British capital here," Laszlo Kovacs, the Foreign Minister, said on the eve of Mr Horn's departure. "And we want to make it very clear that Hungary wants to be in the first wave of Nato and EU enlargement."
Although no timetable has been set for the accession of new members, the Hungarian government believes it is on course to join the military alliance by 1998 and the EU two years later. It thinks negotiations on Nato membership could start in late 1996, after presidential elections in Russia and the United States, and EU talks in early 1998, about six months after the European Inter-Governmental Conference.
Like others in the region, Hungary has been horrified at the increasingly bellicose way in which Moscow has been voicing its objections to Nato expansion and sees the protests as largely directed at a domestic audience.
"Many here undoubtedly feel that the West pays too much attention to Russian concerns [over Nato enlargement]," said Mr Kovacs. "But in our view, while developments in Russia could lead to a slowing down of the process, they could also lead to an acceleration."
As part of its preparation for Nato, Hungary is seeking to improve relations with neighbouring countries containing large ethnic Hungarian minorities. In March a treaty was signed with Slovakia. Attempts to agree a similar treaty with Romania, which has an ethnic Hungarian minority of almost 2 million, have so far failed but Mr Kovacs insisted there was no prospect of an outbreak of inter-ethnic conflict.