It is a good place for naval and other military excercises.
Most of the time they are not active. If you look on the chart narrative it tells you how they are activated (usually by NOTAM) and who to contact. If you check your NOTAMs you will know which ones are cold and / or London Info will usually have the information (or Plymouth mil or Bournemouth LARS if you are further west.
You are not necessarily better planning aroute to avoid them - if they are cold and it suites you go ahead. However, there is a VFR route marked roughly from St Catherines point (where the old CP was) to Cap de la Hargue. It has the advantage of making the crossing about as short as possible if that is a factor for you. Moreover in the very unlikely event you end up in the drink if you are in the VFR corridor everyone will know where to find you.
Jersey zone will never refuse you a transit but the transit will always be SVFR - so it is worth making sure you are familiar with SVFR.
Once you are in the zone Jersey will give you a height and a steer. You must comply (it is a clearance). If you want another route you can ask and are likely to get it, but there is no guarantee. You are very likely to be kept below 2,000 if on a SVFR clearance.
Personally, I think a good route could be Liverpool, Lasham, St Catherine's Point, Orist. That route keeps you clear of Southampton, the airway and the danger areas. (a bit of dodging around the danger areas etc down to Lasham as required).
You will get a service from Bournemouth LARS to 50N - you dont need to speak to anyone else for the crossing and you dont even need a service from Bournemouth if you dont want it - work London if you want a flight watching. Expect to change to Jersey zone just before 50N so make sure you know where it is (they will often ask you to report 50N) and expect them to route you towards the Cap or perhaps direct.
The advantage with this route is there is no height restriction so go as high as you like for the crossing.
Hope that helps.