it would depend on your agreement with the solicitor.
you may have entered into an arrangement where the solicitor has agreed to pay for everything, not be paid anything until the case concludes, but needed the security of holding your monies until the costs had been sorted out (which can take some time) to ensure that the costs would be discharged.
we will presume you have not paid any money on account to date.
i'd doubt whether the costs have been "agreed" as you state, but rather there is an agreement that your "party and party costs" will be paid by the other side - i.e. that your liability for "party and party" costs has been indemnified by the other side. This may not cover all of the costs associated with the case (contrary to frequently quoted belief). Any costs however that you end up funding (rather than the other side) would have to be explained to you.
if the foregoing is accurate it would be possible usually for a solicitor to estimate what the possible costs shortfalls might be and to release the majority of the settlement money to the client, whilst at the same time making sure that they have adequate security of the entire bill being discharged by holding money on account (it is still the client's money). The solicitor's risk of not actually being paid remains in this circumstance. That risk varies depending who the defendant is. if we are talking a personal injury claim (which i'd imagine we are) then there is less risk if the defendant is insured by a major, reputable, insurer (but even insurers have collapsed in the past) - you may not be capable of paying your bill at the time that it became apparent that the defendant couldn't (make no mistake it is still your bill) so your solicitor runs the risk of never being paid.
alternatively perhaps it would be better all round, and possibly more transparent, if the entirety of the legal costs be paid by you now , at this time, from the settlement money, the balance paid out to you, and you can then instruct the solictior to get as much of the costs back for you from the other side as possible pursuant to the order that the defendant pay your "party and party" costs. Your solicitor would prefer this i'd imagine.