Why the hesitation on using code. That's the way to go.

Back up your table data first.

Then add a new field to your table.
Field Name:    [Id]  
Datatype:       Number
FieldSize:        Long Integer.

Then copy and paste the below code into new Module:

Public Sub AddIDNumbers()
Dim rs As DAO.Recordset
Set rs = CurrentDb.OpenRecordset("YourTableName")
Dim lngX As Long
lngX = 100500
rs.MoveFirst
DoCmd.Hourglass True
Do While Not rs.EOF
With rs
   .Edit
   !Id = lngX
   .Update
   .MoveNext
End With
   lngX = lngX + 100
Loop

DoCmd.Hourglass False
Set rs = Nothing

End Sub
************
Run the procedure and it will update your table.

Note: with 292000 records, that last ID value will be 29,300,400.
Are you absolutely sure this is what you want to do?
Why?

UPDATE [TheTable]
SET ID = 100500 + DCount("*","[TheTable]","[Client Name]<""" & [Client Name]
& """") * 100

That will be slow.

Alternative would be to add records to a new table that has the structure
you want using a query like the following.  I think that this should be
considerably faster, especially if you have indexed the client name field in
the existing table.

INSERT INTO NewTable ([Client Name], ID)
SELECT A.[Client Name]
, Count (B.ClientName)*100 + 100500 as NewID
FROM [Existing Table] as A LEFT JOIN [Existing Table] as B
ON A.[Client Name] < B.[Client Name]
GROUP BY A.[Client Name]