Re-entry Belgium in case of Belgium Residence Permit being stolen in London

First things first: do not let this awful experience get to you. Just focus on solvin the problem. Here are the steps you need to take:

1. Go to the police and report your documents as stolen. Give as many details as possible; ideally you should remember your passport number. Even better if ou have scanned copies of the lost documents to show and attach to the police report.

2. You need to get a new passport or an emergency travel document from your embassy/consulate.

3. You will need to apply for a new residency card at the Belgian embassy/consulate in the country you currently find yourself in

Quoting from the linked Belgian website:

En cas de perte ou de vol de la carte d’identité et/ou du passeport à l’étranger, une déclaration doit être faite auprès de la police.

Muni de cette déclaration et de photos d’identité, il vous sera possible d’obtenir un document (provisoire) auprès de l’ambassade ou du consulat belge ou, s’il n’y en a pas, auprès d’une représentation d’un autre pays de l’Union européenne.

La procédure sera facilitée si vous disposez d’une copie des documents égarés ou volés, de leur numéros et/ou de documents permettant de vous identifier (permis de conduire…).

Experience from other travellers indicates that you may be allowed to fly back with just a new passport and the police report. When my colleague had his French residency permit stolen in Prague he was allowed to fly back to France with the police report and his passport. Generally speaking airlines tend to be forgiving in these situations. Now, you are flying between the UK and the Schengen area so you will encounter immigration checks upon landing in Belgium therefore your mileage may vary.

In the future, my advice is that you save a scanned copy of your documents somewhere easily accessible - cloud, email, etc.. Having copies makes filing the police statement, and convincing immigration officers that you had a visa/residency permit much easier.