Hello, welcome to Justanswer. My name is Tony and I can answer your question for you.
I'm afraid you would be liable to pay the bill if counsel's fee was incurred with your consent. However, you might have grounds to argue that the solicitor has delivered inadequate professional services and that as a result you are entitled to report him/her to the Legal Ombudsman. This is something that they might want to avoid and you might be able to use that as a negotiating leverage to reduce what you might pay. Like going half each, paying £300 plus VAT each and calling it a day.