A story in the gemara[1] forms the basis of the answer to your question. After Rav Yehuda recuperated from a severe illness, several rabbis visited him and said: “Blessed is HaShem who gave you to us and not to the earth.” Rav Yehuda responded that they had exempted him from the need to thank HaShem (in other words, to recite Birkat HaGomel). The gemara asks how Rav Yehuda could have been exempted if he had not made the beracha himself and answers that he had responded amen.
A conclusion one can draw from this gemara is that a person can recite Birkat HaGomel on behalf of others. Indeed the Shulchan Aruch[2] rules: “If one recited HaGomel for himself and intended to exempt his friend and his friend listened and intended to be exempted, he (the friend) fulfilled the obligation even without answering amen.” The fact that amen is not required should not be surprising, given the rule that one who hears a beracha from his friend needs only to listen,[3] although it is proper to also answer amen.
Why, then, does the gemara require amen in its case? The Tur[4] cites his father, the Rosh, who explains that, in Rav Yehuda’s case, the people who recited the beracha were not personally obligated to do so, although it was an appropriate reaction because someone they cared about was saved. Under those circumstances, they could not be motzi[5] Rav Yehuda. However, by answering amen, Rav Yehuda was considered to have recited the beracha himself. Rav Akiva Eiger[6] says that the issue was that the language of the well-wishers, who praised HaShem for helping someone else, did not apply sufficiently to Rav Yehuda (who needed to express praise in the first person) unless he answered amen.[7]
In any case, it is clear in the Shulchan Aruch that one can say Birkat HaGomel on his own behalf and have it fulfill the obligation of another person as well. Yet, one can still ask whether it is better to do it as a group or individually. In principle, when one can make a beracha on behalf of others, that is the preferred practice. However, the Mishna Berura[8] raises the point that we usually make berachot individually, perhaps out of concern that either the one saying the beracha or the one listening to it will not have the proper intentions. The Piskei Teshuvot[9] says that the same applies to Birkat HaGomel and that this is the accepted practice.
We agree that each person usually says his own HaGomel when just a few are obligated. If many people are involved, it becomes a matter of tircha d’tzibbura (congregational inconvenience) and, in addition, encourages talking. Thus, it is a common and perfectly acceptable practice for one to recite the beracha after announcing that all others should listen with the intent to be included.
The Piskei Teshuvot[10] makes another claim with which we take issue. He says that the one reciting should use the plural form, saying “… shegemalanu…” (who granted us). His source for this ruling is a case where there was a group salvation; it was not a case where one makes a beracha for a personal salvation and others join in his beracha. If the Piskei Teshuvot were correct, one would have expected one of the Shulchan Aruch’s commentators to point out that the beracha is different. In fact, the Shulchan Aruch’s language strongly suggests no change whatsoever. He describes one who recites Birkat HaGomel “for himself and intended to exempt his friend.” This clearly implies that his wording was appropriate for a personal beracha, and just his intention connected him to his friend. Only in regard to the less formal response of the congregation (“mi shegemalcha…”), which is not discussed in this halacha of the Shulchan Aruch, does it make sense to use the plural form since it includes all of the people covered by the beracha in the wish of continued good fortune.