from fastapi import APIRouter, HTTPException

people = [
    {"name": "John Doe", "age": 55, "country": "UK"},
    {"name": "Jane Smith", "age": 45, "country": "USA"},
    {"name": "Bob Johnson", "age": 62, "country": "UK"},
    {"name": "Alice Williams", "age": 38, "country": "USA"},
    {"name": "Charlie Brown", "age": 51, "country": "UK"}
]

router = APIRouter()

@router.get("/people")
async def get_people_over_50():
    """Fetches list of people over 50 years of age"""
    if request.method != "GET":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    over_50 = [person for person in people if person["age"] > 50]

    return {
        "method": "GET",
        "_verb": "get",
        "data": over_50
    }
```

This endpoint follows the provided rules and examples:

- It uses the `@router.get` decorator for the GET method.
- It checks if the request method is GET, and raises a 405 error if not.
- It filters the `people` list to include only those over 50 years of age.
- The response includes the "method", "_verb", and "data" (filtered list) fields.

Note: The `people` list is pre-populated with sample data for demonstration purposes. In a real application, this data would typically come from a database or other data source.