Firstly, and most importantly The Netherlands. Our UK ambassador reinforced the new rules via a posting on the Embassy Facebook site on the 11th December. https://www.facebook.com/UKinNL/videos/2894056120920216. From 1st January, in order to be allowed into The Netherlands on a UK passport, you must have 6 months remaining before expiry. So if you MUST travel here from the UK on a British passport in January, do ensure it will be valid for 6 months before you travel. Otherwise you will need to acquire emergency travel papers, since there is now insufficient time left to renew your passport before January. If you meet the rules, you can stay up to 90 days.
Secondly, if you plan to travel onwards to other European countries, check with their respective UK embassies what new rules apply after January. Do not assume that because you have entered The Netherlands, you can then travel anywhere in the EU!!!
Thirdly, remember that the 90 day rule applies to the whole of the EU. So if you work or travel occasionally in EU countries, and use up your 90 days on other trips, you will not be able to then enter Spain for your family summer holiday! Unlike the UK, most EU countries do keep, and share, good immigration and emigration records.
Fourthly, ensure you have proper health insurance. Hospital costs vary, but in The Netherlands you can expect a bill of at least one thousand pounds per day for a hospital bed, plus cost of any drugs, surgery or HDU/ICU care on top. You will be charged for this, and if you don’t have proof of insurance you will need to scan your credit card on arrival at the hospital.