The most important thing is to check if your customer is VAT registered. If they are then the general rule is that the place of supply of your service is deemed to take place in the Netherlands and so, as, I assume, you are not VAT registered there, you charge zero VAT and must quote their VAT number and country code on the invoice. You must also add the text: "Article 44 of the EU VAT Directive; VAT is due by the recipient of the service”.
You can do the same if the client is a business and not VAT registered but you must get documentary evidence that they are in business and not a consumer.
If they are a consumer, ie non-business, the place of supply is deemed to be in the UK so you charge VAT as if they were a UK customer.
Whether you charge in Euros or £s is up to you and your client to agree, if you charge VAT though, and invoice in Euros, you must also state somewhere the £ value of the VAT, CB may do this with a Euro invoice, I can't remember.
The above are the general rules on "place of supply" rules for services, there are some exceptions, ie if the work is to do with land then the place of supply is where the land is. Worth a scan of the VAT guide 741A:
This site may also help: https://transferwise.com/gb/blog/invoicing-eu-customers-as-uk-business