I did the exact same thing about a year ago, although I departed Rotterdam instead of Hilversum.
I climbed to FL45 as soon as I was clear of the Schiphol TMA and stayed there until feet dry over dover. My routing was EHRD - COA - KOK - KONAN (is the reporting point at the FIR boundary) - DVR - DET - OCK - EGLK.
This was before the Farnborough LARS so I spoke to London INFO most of the way. They really follow you when you're over the water so make sure you report your position exactly as you were taught. They also communicate with Ostende APP and vice versa so you're never alone. Do bear in mind that London INFO has no radar so it's all done by ear. If London is busy you can also get a RIS from Manston for the crossing.
Between DET and OCK, to remain clear of the EGKB ATZ, I just followed the M25. You can't miss it. It keeps you clear of the ATZ but also of the Gatwick CTA/CTR. Despite this, London asked me to give Biggin Hill a courtesy call.
Blackbushe does an overhead join which is indeed very strange from a Dutch perspective. Although I understand that if you ask and it's not too busy, you can also do a Dutch-style direct downwind entry.
Have you also considered customs? You can fly EHHV-EGLK direct provided that you fax the GAR form four hours in advance to the relevant authorities. I simply faxed the form the day before to EGLK, who (supposedly) fax it onwards to whoever needs it. For the way back, EHHV has customs available with 1 hour PN. So give them a call before departure!
The flight to Blackbushe was my first flight into the UK and in fact my first serious touring flight in Europe. It took me a long time to prepare and find all the information but in the end it was over before I knew it.