I think you'll manage quite well with that budget. You're not travelling through reservation heavy countries, which also saves you some money. You'll be travelling throughout July too, which means holiday season and more expensive prices for accommodation. It might be wise to keep the more expensive places for June, to avoid high season prices.
Except Amsterdam, many of the places you visit are considered rather cheap (you generally skip Western Europe, Scandinavia or Switzerland) . The further (south)east you go, the cheaper it gets.
In July you might want to avoid popular routes on weekends (busy trains) or at least reserve seats. For the rest it seems okay, only getting you in/out of the UK will cost you a bit extra (Eurostar, or the ferry) - presuming you don't fly.
In the end, it all depends on what you do as well on your journeys. If you like hiking, nature and you take a tent you'll be very cheap. If you're more of a city trotter and like museums, and gastronomical pleasures of all sorts you'll obviously spend more money. Probably it's gonna be a combination of both. Enjoying summer in a city, and week later you'll be chilling with your feet in a nice mountain river, in a deserted place with only a book as company.
Although if you choose your accommodation carefully, a hostel with self-catering possibilities e.g., you can cut costs very good as well (presuming you travel solo - in group self-catering units might be a wiser choice).
With a continous pass it's also a good idea to stay in the cheaper outskirts of the city, and take a train to the centre. It'll cost you a bit more time, but no extra budget. Or if you don't find accommodation with acceptable prices, find a smaller town with cheap accommodation a bit further, with good train connections, making it your base of operations for some days.
If you need any other advice of any sorts, like scenic routes, less trodden paths to discover, how to plan trains, which trains we recommend taking or how to avoid (expensive) reservations, or cruising around the more adventurous Balkans, the community is a collective beacon of wisdom happy to help. 😉
Good luck planning!