In general, passports may suffer from wear and tear or damage. Damage typically makes a passport invalid, while normal wear and tear does not.
When you present your passport to someone (an immigration official, for example, or an airline employee), they will have to make a determination. If they decide that the passport is damaged, they will refuse it, and you will be refused boarding, or refused entry.
(Yes, you can be refused entry to the UK if you cannot convince the border officials that you are a British citizen, though in your case it seems you should have no trouble convincing them of this because the personal information page is intact.)
Still, you want to evaluate the risk of being denied boarding on an airplane heading to the Schengen area (or a ferry heading to France or the Netherlands), or of being denied entry once you arrive in a Schengen country.
Your question therefore is "was my passport damaged by the soaking it received, to the point of being invalid?" If it is, you will need to replace it; if it is not, you can use it to travel.
For some example guidance on this question, I checked British and Dutch sources. The British source is a document describing the treatment of worn or damaged passports when they are presented in a renewal application, which you can find at https://www.gov.uk/government/publications/damaged-and-faulty-passports. The document contains this section:
Definition of a damaged passport
A damaged passport is one which is not in a condition to be accepted as proof of identity. Damage may include the following:
- Details are indecipherable.
- The laminate has lifted enough to allow the possibility of photo substitution.
- Discoloration to the biodata page.
- Chemical or ink spillage on any page.
- Missing or detached pages
- The chip or antenna shows through the endpaper on the back cover for the new style e-passports.
- The chip has been identified as damaged following investigation.
The Dutch source was for Amsterdammers deciding whether they need to replace their passports, but presumably Dutch border guards would apply similar criteria. It can be found on www.amsterdam.nl. It reads:
Mijn paspoort, rijbewijs of identiteitskaart is beschadigd. Wat moet ik doen?
Als uw identiteitsbewijs is beschadigd, is het niet meer geldig. U moet dan een nieuw identiteitsbewijs aanvragen. In de volgende gevallen is er formeel sprake van beschadiging:
- Als de kenmerken beschadigd zijn waaraan je kunt zien dat het document echt is, en geen vervalsing.
- Als uw persoonsgegevens slecht leesbaar zijn geworden.
- Als er pagina's loszitten of ontbreken.
Een voorbeeld van zo'n beschadiging is wanneer je niet meer zeker kunt weten dat degene die het document gebruikt ook echt de eigenaar is.
My passport, driver's license, or identity card is damaged. What should I do?
If your proof of identity is damaged, it is no longer valid. In that case, you must request a new one. The following are, formally speaking, damage:
- If the anti-counterfeit measures are damaged to the point that you cannot verify that the document is genuine.
- If your personal data have become difficult to read.
- If pages are loose or missing.
An example of such damage is when you can no longer be certain that the person presenting the document is its real owner.
You can see that the Dutch source mentions both those aspects of the document that are designed to prove that it is genuine and those concerned with identifying the holder, while the British source is concerned only with the latter. To be safe(r), you should probably consider both.
I am reluctant to guess about your chances of having the document accepted, especially since I haven't seen it. For non-EU travel, the fact that stamps have been faded by water damage almost certainly means the passport would be rejected. You might be able to get away with it within the EU, but then again, you might not.
If I were you I'd consider asking a UK guard on entry into the UK whether the amount of damage is acceptable (if they don't bring it up themselves -- I suppose it's possible that they might cancel it then and there). That is, I'd go to a desk with an actual person, present the passport, and once they tell me to proceed, if they haven't brought up the condition of the passport, I'd ask.
If they advise that the passport probably isn't acceptable in its current state, I would get a new passport while in the UK.
Do let us know what you decide to do and what happens.