I can recommend both Blue Rose (I think it is still Enid that you speak) to and also Ghillies (forgive spelling). Have used both and they both are, in my experience, very caring and professional.
They do shared loads. They have both picked up for me in the North and delivered to us in Suffolk. As I requested they put travel pads/bandages on.
www.findhorsetransport.org is quite a good website and you can get a few quotes at a time. When i do my test this week I'll be advertising my new transport business on there
Gillies, every time. I have used them in the past, and they are totally professional.
They are also religious about schedules, lorry maintenance abiding by the rules.
Just a quick thought, I'm sure I've heard LOC's name mentioned in connection with French Rescues, I think one of the sites use them. Not sure I'd be wanting one of my horses travelling with them!