On the assumption that you hold a UK passport and will be starting your journey from within the UK, my understanding is as follows.
If you are planning travel within the EEA then although you will have no difficulty leaving the UK, you have to pass formal immigration controls in all other countries - unless perhaps Ireland (I don't know the present position there). This is because, unlike most of the rest of Europe, the UK is not a member of the Schengen Agreement. Returning to the UK will involve immigration controls leaving the country of departure and again to enter the UK. Of these, only the entry into the foreign country (outward journey) is at all likely to present any form of complication. You will also likely have to show your passport for identification purposes when boarding aircraft in both directions. Travel from country to country within the Schengen Area, by any form of transport, presents no challenge because there are no border controls (except temporary ones in certain locations due to the immigrant crisis). After entering the EEA, you can then travel between Iceland and Portugal via all the countries in between and others well off-route (but not the UK) without ever being asked for documentation by a single immigration/border control official.
Many, probably most, countries within the EEA will let anyone in on a then valid passport - I suspect (but don't know for certain) that at most they would want to see a return ticket for before the expiry of the passport. To be certain, I suggest you contact the embassy in question and ask. The point is that not only are you entitled to enter an EEA country without restrictions but you are entitled to settle and look for work there too (international treaties, until the UK leaves the EU/EEA) - based on possessing (but not necessarily at that point showing anyone) a valid passport as identification on entry and thereafter being able to prove your status as an EEA citizen.
Travel to anywhere other than the EEA is likely to present serious obstacles and for lots of countries you would be required to have at least six months validity remaining on your passport when entering.