You might be in luck - even though Tunisian citizens require a visa to leave the airside area of the UK's airports, there's a subclause:
Nationals of ALL countries (RED [underlined] and BLACK above) need a
visa to transit LANDSIDE unless they hold one of the following: (i) a
valid visa for entry to Australia, Canada, New Zealand or the USA and
a valid airline ticket via the UK as part of a reasonable journey TO
(Tunisia is listed in black.)
If you have a visa for your USA visit, you should be ok. I'd check it with your local UK consulate/embassy though to be certain, as "a guy on the internet told me" isn't a threshold many customs officers respect.