To optimise the cost of VMs running in Azure, the ability to downsize a VHD in Azure without copying it back on-prem or using 3rd party tools was essential.

The Windows 10 images from the Azure market place come at the standard size of 128GB, which is too big for a basic Win10 VM used for VDI.

First create an empty disk against any existing Windows VM you have in Azure:

# This creates an empty 32GB disk against an existing VM in an existing Resource Group  
$VMName = "vm-resize-disk"  
$RGName = "rg-resize-disk"  
$DiskSizeGB = 32

write-output "Getting StorageAccount for $VMName"  
$URI = ((Get-AzureRmVM -ResourceGroupName $RGName -Name $VMName | select StorageProfile -ExpandProperty StorageProfile).OSDisk.Vhd).uri  
$StoreStr = ([System.Uri]$URI).Host.Split(".")[0]  
write-output "Storage account is: $StoreStr"

$ContainerStr = ([System.Uri]$URI).Segments[1].Trim("/")  
write-output "Storage account OSDisk container is $ContainerStr"

$Store = Get-AzureRmStorageAccount -Name $StoreStr -ResourceGroupName $RGName  
$StoreKey = (Get-AzureRmStorageAccountKey -ResourceGroupName $RGName -Name $Store.StorageAccountName)[0].Value  
$StoreContext = New-AzureStorageContext -StorageAccountName $Store.StorageAccountName -StorageAccountKey $StoreKey

$Contain = Get-AzureStorageContainer -Name $ContainerStr -Context $StoreContext

$VM = Get-AzureRMVM -Name $VMName -ResourceGroup $RGName

Write-Output "Adding empty $($DiskSizeGB)GiB disk to VM $VMName..."  
Add-AzureRmVMDataDisk -VM $VM -Name "$($VMName)-empty" -VhdUri "$($Store.PrimaryEndpoints.Blob)$($Contain.Name)/$($VMName)-empty.vhd" -DiskSizeInGB $DiskSizeGB -Lun 0 -CreateOption Empty -Caching None  
Update-AzureRmVM -ResourceGroupName $RGName -VM $VM

Write-Host "Removing empty disk from VM $VMName..."  
Remove-AzureRmVMDataDisk -VM $VM -DataDiskNames "$($VMName)-empty"  
Update-AzureRmVM -ResourceGroupName $RGName -VM $VM

Next, we will use the empty disk set as 32GB, to resize the existing osdisk of the VM.
It goes without saying, the VM must be shutdown and deallocated first and also make sure you have shrunk the disk size in Windows to 32GB or below:

# Change the -osdisk VHD file to new size (32GB)  
# Note: make sure you have shrunk the disk from Windows to 32GB or below first  
$VMName = "vm-resize-disk"  
$RGName = "rg-resize-disk"  
$StorageAccountName = "sa-resize-disk"  
$ContainerName = "vhds"

write-output "Using StorageAccount $StorageAccountName"  
write-output "Using Container $ContainerName"

write-output "Getting storage account $StorageAccountName into variable"  
$Store = Get-AzureRmStorageAccount -Name $StorageAccountName -ResourceGroupName $RGName  
write-output "Getting storage keys for $StorageAccountName"  
$StoreKey = (Get-AzureRmStorageAccountKey -ResourceGroupName $RGName -Name $Store.StorageAccountName)[0].Value  
write-output "Creating storage account context"  
$StoreContext = New-AzureStorageContext -StorageAccountName $Store.StorageAccountName -StorageAccountKey $StoreKey

$Contain = Get-AzureStorageContainer -Name $ContainerName -Context $StoreContext

write-output "Getting properties of OSDisk"  
$OSDiskVHD = ($VMName.ToLower())+"-osdisk.vhd"  
$osDisk = Get-AzureStorageBlob -Context $StoreContext -Container $contain.Name -Blob $OSDiskVHD

write-output "Getting properties of the empty disk"  
$emptyDisk = Get-AzureStorageBlob -Context $StoreContext -Container $contain.Name -Blob "$($VMName)-empty.vhd"

$footer = New-Object -TypeName byte[] -ArgumentList 512  
write-output "Get footer of empty disk"  
$downloaded = $emptyDisk.ICloudBlob.DownloadRangeToByteArray($footer, 0, $emptyDisk.Length - 512, 512)  
$footerStream = New-Object -TypeName System.IO.MemoryStream -ArgumentList (,$footer)  
write-output "Write footer of empty disk to OSDisk"  
$osDisk.ICloudBlob.WritePages($footerStream, $emptyDisk.Length - 512)

#write-output "Deleting empty disk VHD"  
#Remove-AzureStorageBlob -Context $StoreContext -Container $contain.Name -Blob "$($VMName)-empty.vhd"

Massive thanks to @rupertbenbrook for pretty much all of this great and very useful code.

Note: Please check with Microsoft support before implementing this in a production environment if you want to be sure it is a fully supported way of changing VHD sizes.