Is there a better way of writing this action method using Linq?

Oliver's looks simple, but you are nesting if statments, which gets really messy.

I also don't like having the numbers array created everytime this method is called. The numbers array should be move to a class readonly Static, saving memory and processing time to create it.

the but IF...else...else statement should be moved to a switch, keeping the code much cleaner.

You don't have to, but I like the pattern of using a dictionary (again, static readonly) with and enum to determine which branch to use.

Instead of getting the count from the source list, get the count from the items returned. This will eliminate one call to the source every time this method is called. I added the .ToList() to the end of the query to make sure the list is stored in memory, so the .Count will not query the data source again.

I also created a method to return your list, this way your declaration and assignment are much closer together, making the method much easier to read.

I can also see a problem with using All, there might be circumstances where it conflicts with a general string query. I would suggest moving the matching patterns in my dictionary into some kind of parsing routine (Regex maybe?) to make sure you are not stepping on toes so to speak. This will also shorten the dictionary to 3 entries.

Anyways, my solution follows:

private enum FilterType
{
    All,
    PartNumber,
    StringQuery
}

private static readonly IDictionary<string, FilterType> AcceptableFilters =
    new Dictionary<string, FilterType>
        {
            {"All", FilterType.All},
            {"123", FilterType.PartNumber},
            {"A", FilterType.StringQuery},
            {"B", FilterType.StringQuery},
            {"C", FilterType.StringQuery},
            {"D", FilterType.StringQuery},
            {"E", FilterType.StringQuery},
            {"F", FilterType.StringQuery},
            {"G", FilterType.StringQuery},
            {"H", FilterType.StringQuery},
            {"I", FilterType.StringQuery},
            {"J", FilterType.StringQuery},
            {"K", FilterType.StringQuery},
            {"L", FilterType.StringQuery},
            {"M", FilterType.StringQuery},
            {"N", FilterType.StringQuery},
            {"O", FilterType.StringQuery},
            {"P", FilterType.StringQuery},
            {"Q", FilterType.StringQuery},
            {"R", FilterType.StringQuery},
            {"S", FilterType.StringQuery},
            {"T", FilterType.StringQuery},
            {"U", FilterType.StringQuery},
            {"V", FilterType.StringQuery},
            {"W", FilterType.StringQuery},
            {"X", FilterType.StringQuery},
            {"Y", FilterType.StringQuery},
            {"Z", FilterType.StringQuery},
        };

private static readonly IList<string> Numbers = new List<string>
                                                    {"1", "2", "3", "4", "5", "6", "7", "8", "9", "0"};

[HttpGet]
public ViewResult Index(int page = 1, int pageSize = 30, string filter = "All")
{
    // This checks that the filter value received by the method is an acceptable value.
    // E.G. If a user types in a value in the query string that is not contained in the
    // array above, then the filter is reset to 'All' and all records are queried.
    if (!AcceptableFilters.Keys.Contains(filter))
    {
        filter = "All";
    }

    var parts = RetrievePartsAccordingToFilter(filter);
    var totalParts = parts.Count;

    var viewModel = new PartsListViewModel
                        {
                            Filter = filter,
                            PageInfo = new PageInfo(page, pageSize, totalParts),
                            Parts = parts,
                        };

    return View(viewModel);
}

private IList<Part> RetrievePartsAccordingToFilter(string filter)
{
    switch (AcceptableFilters[filter])
    {
        case FilterType.All:
            return (Database.Parts
                .OrderBy(p => p.Number)
                .Skip((page - 1)*pageSize)
                .Take(pageSize)).ToList();
        case FilterType.StringQuery:
            return (Database.Parts
                .OrderBy(p => p.Number)
                .Where(p => Numbers.Contains(p.Number.Substring(0, 1)))
                .Skip((page - 1)*pageSize)
                .Take(pageSize)).ToList();
        default:
            return (Database.Parts
                .OrderBy(p => p.Number)
                .Where(p => p.Number.StartsWith(filter))
                .Skip((page - 1)*pageSize)
                .Take(pageSize)).ToList();
    }
}