First of all, it is very important to report your stolen passport to the police, this can be done using this service which is accredited by UK police. The UK Government advises all stolen passports to be reported.
Next, you need to call the embassy in Paris or Lisbon and explain the situation as to replace your BRP you need a passport.
They might let you replace it at an embassy in London or offer an alternative solution like mentioned in the comments to replace it by mail, the only way to get a definite answer as to what to do is by contacting them.
Next, you need to report your BRP as stolen and apply for a replacement (if you don't do this you could face a fine), as mentioned on the GOV website:
If you’re in the UK
If your lost or stolen BRP was valid for 3 months or more, report it and apply for a replacement. You must do this within 3 months of losing it.
You can be fined up to £1,000 and made to leave the UK if you do not apply for a replacement within 3 months.
If it will expire in the next 3 months according to the GOV website you need to:
If your BRP was valid for 3 months or less, you must do one of the following:
- report it as lost or stolen if you do not intend to remain in the UK after its expiry date
apply for a replacement if you plan to leave and re-enter the UK within 3 months of its expiry date
apply to extend your visa if you want to stay in the UK after its expiry date - if granted, you’ll automatically get a new BRP