This part is incorrect: GMT+0100. It should be GMT+01:00 or GMT+1:00 per the Unicode standard for localized GMT format. You can correct that however you like and then the below code should work.

Alternatively (and perhaps easier), you could change the GMT part to UTC in which case the basic ISO8601 time zone format UTC+0100 will work.

import Foundation

struct TestStruct: Decodable {
    let name: String
    let activity: String
    let date: Date
}

let rawJSON = """
[
    {
        "name": "Charlotte Grote",
        "activity": "Solving",
        "date": "Sat Aug 20 2022 12:30:00 GMT+01:00 (British Summer Time)"
    },
    {
        "name": "Shauna Wickle",
        "activity": "Baking",
        "date": "Sat Aug 20 2022 12:30:00 UTC+0100 (British Summer Time)"
    }
]
""".data(using: .utf8)!

let fmt: DateFormatter = {
    let fmt = DateFormatter()
    fmt.dateFormat = "E MMM dd yyyy HH:mm:ss ZZZZ '('zzzz')'"
    fmt.locale = Locale(identifier: "en_US_POSIX")
    return fmt
}()

do {
    let decoder = JSONDecoder()
    decoder.dateDecodingStrategy = .formatted(fmt)
    let test = try decoder.decode([TestStruct].self, from: rawJSON)
    test.forEach {
        print("\($0.name) - \($0.activity) at \($0.date)")
    }
} catch {
    print(error)
}

Outputs:

Charlotte Grote - Solving at 2022-08-20 11:30:00 +0000
Shauna Wickle - Baking at 2022-08-20 11:30:00 +0000