Should we book Eurostar when plane may be delayed?

If you miss the train, you’ll have to buy a new ticket.

You may find the discussion here helpful--- https://community.ricksteves.com/travel-forum/general-europe/landing-in-london-then-eurostar-to-paris

Have you considered flying to Brussels from Heathrow?

I agree with the previous reply to look into flying to Brussels from LHR. Just the hassle factor of clearing customs, getting to St. Pancras, going back through security for the Eurostar and then the travel time and cost of the Eurostar ticket is enough for me to seriously consider the flight. Even if it cost a little more, I think it would be more than offset by less stress and hassle.

your times should work unless somebody with a big spanner throws it in the works...

or you could fly but then you'd be cooped up again

that's what travel insurance is for

If everything goes as planned, it should work. But there is always the possibility of something unexpected happening, so it depends och how much risk you are willing to accept. If you are delayed, you need to buy a new train ticket.

The big question in my mind is why you are flying to London if your destination is Brussels.

Be cautious about flying the short leg. Some discount airlines use an inconvenient alternate airport other than BRU. For my direct flights from the east coast US to LHR, I would buy the 3PM train you named, if you have already bought the LHR ticket.

On my last LHR arrival, the electronic immigration gate was faster than returning to the USA, without enrolled immigration accelerators.

Your question is a bit short of information to get the best answers: Month of year, originating city, cities on the trip, nationality, number of segments in your journey before LHR, class of travel, whether this is your first international trip. No hacker can track you down and steal your retirement money, from telling us that information.

I think that you are cutting it a bit short on time to get the 3 pm train. You might make it, but it will be a stressful time.

Yes, we have considered flying. Thank you for the suggestions and heads up on airport other than BRU.