This is between you and your solicitor, so the question is, will he sue you if you refuse to pay (and will he win that suit). A good place to look is the agreement which you have with the solicitor, where you promise (or don't promise) to pay certain costs. There could be a clause which addresses your question, saying that the client is responsible for actual costs of third party services secured by the solicitor on client's behalf. Even if there is no such clause, a reasonable person would interpret the situation so that the client is responsible for paying the insurance premium in such a case. Your argument would have to be that you would not have agreed to select Brand X rather than Brand Y in light of the difference in cost. This assumes that there is a competing policy that is functionally the same (or better) but cheaper. You also have to show that if you had known the correct price, you would have instructed the solicitor to do something else -- refuse to provide the policy? keep shopping?
I understand that when you're paying someone else to pay attention to these details that it is irksome when they don't pay attention to the details (you might at least ask for an explanation of why he gave you the wrong price), but an innocent error does not entitle you to a bit of enrichment at the solicitor's expense. If there is something about the matter that constitutes professional incompetence, then the story would be different. In general, one can always claim "If I had but known, I would not have ..." but I (putting myself in the place of a juror evaluating your estoppel claim) am not persuaded that you would have acted differently. 115 pounds is not a shocking difference in price, and since the price of these policies is not easy to get from casual investigation (you can't Google it), if you had been given the correct price initially, you still would have paid that price (rather than let the sale go down the tube). So I think it would be very difficult for you to make the case that you are not liable for the difference in price.