Sub integrate()
    'Add a new sheet
    Set newSht = Sheets.Add
    newSht.Name = "All"
    Set newRg = [a1]
    
    'Go through all sheets and skip the new sheet named
    For Each sht In Worksheets
        If sht.Name = "All" Then GoTo skip
        sht.Activate
        If sht.Cells(1, 1) = "" Then
            findFirstCell(sht.Cells).Select
            Set rg = ActiveCell.CurrentRegion
            Set newRg = newSht.[a1].CurrentRegion
            Range(rg(2, 1), rg(rg.Rows.Count, rg.Columns.Count)).Copy newRg(newRg.Rows.Count + 1, 1)
        End If
skip:
    Next
End Sub

Function findFirstCell(InRange As Range) As Range
'This finds the start of the first block of data on the sheet.
    Dim C As Long, R As Long
    R = InRange.Rows.Count
    C = InRange.Columns.Count
    
    For i = 1 To InRange.Columns.Count
        Set findFirstCell = InRange.Cells(1, i).End(xlDown)
        If findFirstCell.Row < R Then
            Exit Function
        Else
            Set findFirstCell = InRange.Cells(i, 1).End(xlToRight)
            If findFirstCell.Column < C Then
                Exit Function
            End If
        End If
      
    Next
    Set findFirstCell = InRange.Cells(1, 1)
End Function