Issues transferring email domain name

Issues transferring email domain name

I recently left Siteground (web & mail hosting). I have managed to move my web domain name to another provider, but my own domain name email address is proving very difficult to deal with. Since leaving - I cannot access my cPanel through Siteground and they're not being very helpful (2 weeks now).
I wish to access my mail ( support@tinkers-cove.com) through zoho and cannot change my CName details.
Siteground have stated:

 For example, the other email host that you're planning to use
Nayden N.: If they have NS to which you can point the domain name, then all you need to do is obtain that information from them and provide it to us
Nayden N.: We will switch the NS records for the domain name , so that it's email services can be handled by the remote provider.

I really need to sort this and any help would be greatly appreciated.
Many thanks,
Nick Robinson