Looking it up I see this is part of a section on ancient bronzemaking, so I'm guessing Ackroyd's logic is that people from contemporary Troy or Egypt may have visited to acquire tin. It's true that the British Isles was one of the few sources of tin (an essential component of bronze) in prehistoric Europe. And we know from ancient sources that the Greeks got their tin from the far to the northwest:

I have never found anyone who could give me firsthand information of the existence of a sea beyond Europe to the north and west. Yet it cannot be disputed that tin and amber do come to us from what one might call the ends of the earth.

—Herodotus, Histories III

Many people speculate that the "Tin Islands" (Cassiterides) Herodotus mentions here were in fact the British Isles. Whether that's true or not, it's certainly plausible that British tin circulated as far as the Eastern Mediterranean.

However, I'm going to part ways with Ackroyd and say it's unlikely that emissaries or traders from the Eastern Mediterranean ever visited the British Isles in person. Herodotus might concede that tin comes from Northwest Europe but he has so little firsthand information on it that he's not willing to say for certain that the Atlantic Ocean exists, never mind some quasi-mythical islands in it. It's not until the voyage of Pytheas' in the 4th century—well after the end of the Bronze Age—that we have an account of someone from the classical world actually visiting Britain. Also bear in mind that even Herodotus' vague account was written nearly a thousand years after the reign of Akhenaten and the fall of Troy.

I think what's more likely to be going on is something that's commonly observed in prehistory: goods moving more easily than people. If British tin did reach the Eastern Mediterranean, it will have been through a number of middle-men: perhaps across the Channel, through Central Gaul, down the Rhône and on to the Mediterranean via Massilia; or along the coast from Cornwall to Brittany to Galicia (other major tin-producing regions) and thence to Phoenician traders at the Strait of Gibraltar. Many groups would have been involved in down-the-line trade like this, obscuring where the tin ultimately came from. Even if people at the end of the line did get solid information on its origin, they'd have little reason to go there themselves; any possible economic benefit to "cutting out the middle-man" would be outweighed by the incredible risk in undertaking such a long and arduous journey through territory controlled by pissed off middle-men.

u/brigantus has given a very useful answer already, and I don't intend to just repeat it all. However, there's one or two little extra considerations I would raise, namely amber, and the continuing use of tin after the LBA:

The Herodotus reference is of interest for its reference to amber as well as tin, since amber is another trading good for which British Bronze Age cultures such as the Wessex culture are known, and amber thought to be British in origin was discovered at Mycenae, the largest of the Greek LBA cities that were contemporary with Troy (and seat of Agamemnon, the king who led the Greeks against Troy in myth). But would this mean direct trade (for which something like am embassy might be established)? Almost certainly not. If there was direct trade between Britain and the Aegean we would expect there to be other mutual material culture. Amber seems to have been an elite item that made its way to the figures at the top of powerful societies in the eastern Mediterranean, and such items often take circuitous routes to their final owners. It is most likely that it worked its way across Europe via smaller distance trade, as has been explained very nicely in the other answer.

Tin is another consideration. Likewise, it may well be that tin was passed along trade routes in a similar fashion before reaching the eastern Mediterranean. But Troy and Egypt would have had other sources of tin. In the EIA, when previously a tin shortage had been posited, there are in fact example of new bronzes, sometimes with quite high tin content. This is a time when long distance trade is considerably minimised and yet tin is still in supply. It is unlikely that it was regularly coming from as far away as Britain.