The liability to pay is yours, even though the solicitor pays the disbursement for you. If you don't pay, then your solicitor could pursue you for payment through the courts.
There are some disbursements, such as Stamp Duty Land Tax and Land Registry Fee which, if you are getting a mortgage, you must pay your solicitor for, prior to completion or else the terms of the mortgage will mean you are not allowed to complete until they are paid to your solicitor.