Overwintering annuals

Annuals are called that because they generally live only one year. If they are summer annuals, they are unlikely to survive the winter under any conditions no matter how well protected. Perennials, however, live more than one year.

Petunias are short-lived perennials. They are best treated as annuals.

Pelargoniums are perennials. Tender, they are treated as annuals in climates that involve freezing winter temperatures. However, they might indeed thrive under glass. Since I live in a mild-winter area, I have no experience with such protection.

There are many forms of begonias -- over 1,800 species plus hybrids -- all of which are perennial. I have wax-leaf begonias in my garden, blooming all year long. They generally survive my winters without any protection, but they will not survive freezing. Tuberous begonias and hardy Asian begonias go dormant in the winter; both should be protected from freezing, either under glass or with a thick mulch. Etc, etc. Since you are apparently in the U.K., check with a local garden center that knows your climate about what variety of begonia you have and how to keep them during the winter.