Here are a few ideas from me (in alphabetical order):

24-Seven Limo Service
Absolutely Fabulous Limousine (Ab Fab Limo?)
Absoluxe Limo Service
A British Limo Service
A British Accent Limo Service
All Deluxe Limo Service
All Event Limo Service
All Occasion Limo Service
All Seasons Limo Service
Any Event Limousine
A-Plus Limo Service
Aristo Limousine
Beefeater Limousine
Best British Limousine Service
Best o' British Limo Service
Black Tie Limousine Service
Britannia Limousine Service
Buckingham Livery Service

Of course, any of them could be called 'Limo', 'Limousine', or 'Livery', with or without the addition of 'Service' (or 'Company', etc.). So whatever you think of or have suggested to you, try out the sound of it in different combinations.

I hate to repeat myself, but Best o' British to you in your new venture!

And congratulations!