I'd say search for a reputable host. Depending on how quick you can pick things up, I'd say start with managed dedi.
Where will the majority of your clients be based? If mostly UK, try to find a provider in the UK.
As you are already hosting some clients, I'd stick with the same control panel.
The industry standard is cPanel although I quite like Direct Admin as it is less of a resource hog.
Will you be providing any extras to your customers? Fantasico, Installatron, RVSiteBuiler ect?
Do you have an uptime guarantee with your existing clients? If so, be careful when you make the move. Make sure you notify them a while in advance. You don't want unhappy customers or you will have no customers.
Have you already got a website to work from? If not, you need to think of your brand name ect. You also need a billing script. I would recommend WHMCS. It's pretty cheap and included billing and support. If you are offering live support, try livezilla. It's free and works pretty well.
Hope all goes well.