Differs for everyone. Males often learn quicker as the skills needed to drive are found in their play as children (toy cars, computer games with driving or flying etc, sports which require planning, timing, anticipation and judgement) whereas females tend to be more empathic and emotive (caring for dolls, pretending to cook etc). Some people are naturally adept at driving, others simply can't co-ordinate their hands and feet in the right way to react to what they see and feel. You could be test ready within 12-18 lessons, so depending how many you do a week, you could do a test almost straight away if you do well, are taught well, and can get a booking. One tip, do 2 hours at a time. At the start of each lesson there's always some chatting, and the same at the end, and maybe a drive to a suitable practise area depending on what you're working on. If you do single hours then you lose this time every lesson, whereas if you do 2 hours you minimise this lost time. You would probably get too tired to do more than 2 hours as it can be quite draining.
It'll take at least a couple of months, but it ultimately depends on how quickly you learn and also how many lessons you take.
But make sure you take your lessons regularly, like once a week, and get as much practice as you can. Also, it really helps if you have a good instructor too!
But good luck and hopefully you'll be driving on the open roads soon one day!