If their company name is North East Wedding Planners then you are indeed using their business name in promoting your own.
Here's their site for reference:
North East Wedding Planner
The internet address even includes that phrase.
Also they have copyrighted it as can be seen at the bottom of their homepage.
Also they have been established for over 15 years which gives them Prior Art in the name game.
Better to back of quickly now and save any further expense.
As I said earlier you need to write and apologise about the honest mistake you have made.