I totally understand your concerns about tax liability. Generally, if you're a UK tax resident, you'll be liable for UK tax on your worldwide income. When you move to the Netherlands, you might become a tax resident there, too, which could result in dual taxation. However, the UK and the Netherlands have a double taxation agreement to prevent double taxation, so that's a relief.
Regarding freelancing in multiple European countries, you typically need to consider the tax and legal regulations in each country you work with. It's often necessary to set up specific arrangements for each one.
As for your move, have you considered checking out the Three Movers average cost? They might have some helpful tips for relocating your practice smoothly.

Congrats on going full-time! Networking is key, so connect on LinkedIn and reach out to potential clients. Build a solid portfolio to showcase your skills. Good luck!