It's possible, but it isn't easy. Also, it's changing.
Currently, the starting point depends on whether you have a degree already. If so, and really it will need to be a 2:1+, you can take a 1 year Graduate Diploma in Law, after which you can take a second 1 year course towards becoming either a solicitor or a barrister. Both courses are expensive and don't actually get you a job, let alone one in your chosen area.
If you don't have a degree or you have one that's not 2:1+, you're likely to need to take a full 3 year law degree instead of the first 1 year course and, again, get at least a 2:1+, preferably from one of the better universities. Part-time and distance learning course are available, but will obviously take longer, though they allow you to keep earning.
If you've done well, then you will need to get a training job, and at the moment they are hard to come by; that doesn't look likely to change in the near future. Training jobs usually require that you do a wide variety of legal work. After the training job you will need to find a job in medical negligence. There your nursing may stand you in good stead as you will be able to talk the talk. You may also need to decide whether you want to work for claimants or defendants, as a lot of lawyers in that field specialise in representing one or other, not both.
Solicitors are in the process of changing such that technically entry will be based on exam performance without the need for specified degrees or post-graduate courses, but the reality is likely to be that in order to pass those exams you will need to do courses and employers are still want to see evidence of a good degree.
Alternatively you can, as suggested, qualify through on the job training with some day release study as a legal executive or as a solicitor through a legal apprenticeship. These will also take longer.
If it is something you really want to do, then go for it. But you need to be clear that, although it can be very enjoyable, it will be a long, difficult and expensive process.