Try:
Norfolk Line to Dunkerque -
http://www.norfolkline.com/ferry/ - in France, but close to the Belgian border - looks to be about £10 each way
or Stena -
http://www.stenaline.co.uk/ferry/ - to Calais, which is a larger port than Dunkerque, and may have better connections to the Netherlands. They also do Harwich to Hook of Holland - £22 each way for a foot passenger, but it will get you straight there (from Birmingham, you might get a coach straight to Harwich rather than via London)
or SpeedFerries -
http://www.speedferries.com/ - Dover to Boulogne - fast catermaran, but Boulogne is a little further away from the Netherlands. Also looks to be £10 each way.
Since you have time, be sure to look for off-peak fares - 2 months time will be the height of the holiday season, and they may charge extra for the popular times, eg Friday-Sunday (though that may not apply to you as a foot passenger - it tends to be cars that limit them, I think).
Can't help with transport from France to the Netherlands, I'm afraid. You might also get something with the Eurostar train -
http://www.eurostar.com/dynamic/index.jsp - London to Brussels, which leaves you with a very easy way to get to the Netherlands (trains or, undoubtedly, coaches). That looks like you can get a fare about £30 each way (they'll quote prices in US dollars too, but it looks to me as if the exchange rate they use isn't good for you)