I agree with the other doctors that I would not travel more than one hour or 90 minutes away from where you had surgery. The doctor will want to see you the next day and any longer travel invites trouble with bleeding and blood clots in the legs.
All surgical procedures, even one with as low of a risk as a breast augmentation, have some risks associated with them. For this reason, I see almost every client the following day, and recommend that they remain in close proximity for the first night following all general anesthesia procedures. Even though Bristol to London is a relatively short distance, I would continue to recommend an overnight with a responsible adult the first night near your surgeons office. The first day can have some unpleasantness with pain, nausea, etc that a longer drive can contribute to a less pleasant experience. An overnight also means you are close in the event that a complication such as hematoma was to develop. In my opinion the safest option is always the best, an an overnight stay in a nearby hotel is a small price to pay for peace of mind. Good luck with the surgery.
My general advice is that most patients stay nearby for at least the first night after general anesthesia. For relatively short distance drives (1-2 hours), driving home after surgery may be a feasible option. Pain, nausea, vomiting, and grogginess after surgery is expected to various degrees and may be poorly tolerated in a long car ride. It would be important to protect the surgical site, avoid long periods of immobilization to avoid a blood clot, and have a back-up plan in case the patient does not feel up to the (roughly 2 hour?) drive. Realize that in the event of any urgent situation, it would be your responsibility to either return immediately to your plastic surgeon, or obtain care in your hometown, with the potential of additional financial obligation. Hope that helps.
It is wise to stay back for 24 hours in the same location. This will help to see the extent of pain, bruising and swelling. Severe pain and signs of haematoma may require immediate medical attention.
I do not know how far the two cities are from each other, but if it is a long distance I would consider staying local.
Not knowing how far Bristol so from London, the best advice I can give is that I would not allow my daughter to travel more than an hour or so after surgery of any kind on the day of surgery. This is because both surgery and travel increase the risks of blood clots in the legs that can break loose and go to the lungs. This can be fatal. Also, it is better to allow the anesthesia to wear off before any real travel in order to reduce nausea that is both unpleasant and can cause bleeding around the implants. Therefore, if Bristol is any significant distance from London, let her stay in London until her initial post op visit.
It is generally advised to have an one night stay at the hospital post the surgery as it gives your daughter a better recovery.