So, you're both 21 and I presume still planning to do the complete itinerary within 4-5 weeks, starting from July 5, as mentioned in earlier threads.
London - Amsterdam - Fly Easy Jet or similar, see www.skyscanner.com.
Amsterdam - Paris - Trains always pass through Brussels. If you want to stop and see it, then you need separate tickets or seat reservations.
Paris - Munich
Munich-Venice
Venice-Rome
If the travel dates from departing Amsterdam to arriving in Rome fit within 1 month (such as from July 10 to August 9), then you can get a 5-day flexi Global youth pass for $340 per person. Or if you travel Amsterdam-Paris on a direct Thalys train without stopping in Belgium, then you can use a 4-country Select pass for France, Germany, Austria, and Italy for $310 per person. If ordering any of these soon, then be sure to use our $50-off coupon code. You should make seat reservations to and from Paris in the same booking, to be sure that they're available. Seat reservations for all four legs add up to $65 or 70 per person in 2nd class.
You can also fly more legs or you can explore what advance discounts are currently available for booking reserved train tickets a month out. Full-fare tickets cost over $500 in 2nd class (not including London-Amsterdam).