Depending on the industry you work in, it may or may not be common practice for companies (especially larger ones) to have a well-defined recruiting process for candidates living in other countries. This typically involves a few phone or Skype interviews followed by an on-site interview or day of interviews.
There isn't really a difference in how you approach this - just apply as you normally would and be open about your situation when it comes up (don't "request a Skype interview", just say you currently live in the Netherlands and roughly when you plan to move to the UK - the implication there is clear).
If you don't require work sponsorship (i.e. a work permit), it's important to mention that to potential employers, as you can still work for companies that don't provide that (for your specific scenario, it's probably less important to mention, as employers would likely know this already, but there isn't much harm in casually mentioning it anyway).
Alternatively, you can consider arranging let's say a month-long trip to the UK at your own expense (depending on how much leave you have and/or can afford and when you're actually moving). Then contact recruiters or apply for jobs directly with the intention of having the interviews take place during your stay there. I haven't personally done this, but I know people who this has worked for. In theory, some employers may not want to fly you over despite being eager to interview you.