The other driver's insurance company will pay for the damage to their vehicle, and for any medical costs if they were injured, out of the fund which is set aside for compensating victims of accidents caused by uninsured drivers.
That fund will then seek to recover the money from you. So, if you simply dented the other driver's car, expect a bill for a few hundred, or a few thousand, pounds. If you left the other driver injured, and requiring life-long medical care, expect a bill for a few million pounds. The fund will do everything possible to get the money from you, including taking you to court and, if necessary, sending bailiffs to seize your possessions, or making you bankrupt.
If the police and Crown Prosecution Service are currently unaware of the accident, the insurers will notify them that you were driving without insurance. You will be summonsed to appear before a court, where you'll get a criminal record, receive between 6 or 8 points on your licence (or possibly a disqualification from driving) , plus a hefty fine (which will depend upon your income but could be up to �5000), plus court costs (of perhaps �80) , plus a 'victim surcharge' of �15.
Chris