Just to point to the primary sources here (an occupational hazard for me). The issued within last 10 years at time of entry and 3 months remaining at time of departure for third country nationals entering the Schengen area are summarised
here.
These come from
Regulation (EU) 2016/399 [Schengen Borders Code] at Art 6 (Entry conditions for third-country nationals) which specifically says: (a) they are in possession of a valid travel document entitling the holder to cross the border satisfying the following criteria:
(i) its validity shall extend at least three months after the intended date of departure from the territory of the Member States. In a justified case of emergency, this obligation may be waived;
(ii) it shall have been issued within the previous 10 years
Others have already offered helpful practical advice. Worth noting that heading out from London you don't pass a UK border (we don't do manned exit control), but there is a person that will scan your exit under Eurostar's obligation to the Home Office. You will then see the French border post in front of you at St Pancras and will get your wet ink stamp for entry (Art 11 of the same regulation). On the way back it is essentially the reverse, other than the fact you will be greeted by the Belgian border post first (who will stamp you out of Schengen) and then the UK border. I have omitted the security check part in the process for simplicity.
Have a good trip when it comes!