No, that's not necessarily possible. You don't have a right to appeal a refusal like this; the lawyers must apply for judicial review and seek permission of the Court to do the review. That can be done relatively quickly but I doubt it can be done in less than a month. You'd then have to re apply for a visa.
I'm concerned that your consultants are lying to you. Demand that they give you a copy of the petition to the court and proof they are actually applying for judicial review.
I'm concerned that your consultants are lying to you. Demand that they give you a copy of the petition to the court and proof they are actually applying for judicial review.